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4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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4th INTERNATIONAL CONFERENCE ON ANALYSIS
AND ITS APPLICATIONS
SEPTEMBER 11-14, 2018, KIRSEHIR / TURKEY
Abstract Book
Editors
Prof.Dr. Vatan KARAKAYA
Rector of Kırşehir Ahi Evran University
Kırşehir, TURKEY
Prof.Dr. Mohammad MURSALEEN
Aligarh Muslim University
Aligarh, INDIA
Prof. Dr. Necip ŞİMŞEK
İstanbul Commerce University
İstanbul, TURKEY
Prof.Dr. Qamrul Hasan ANSARI
Aligarh Muslim University
Aligarh, INDIA
ISBN : 978-605-85712-8-0
Kırşehir Ahi Evran University, Kırşehir / TURKEY - 2018
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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FOREWORDS
Dear Conference Participants,
First of all, I would like to thank you for coming today to participate at this opening ceremony and I wish
to welcome you to Turkey and Kırşehir. I hope we will have a good time during this conference.
Kırşehir Ahi Evran University was founded on March 17, 2006 in Kırşehir which is located in the center
of Turkey. With approximately 22 thousand students and more than 800 academicians, our university is
a young and dynamic university. Our university consists of 39 academic units, including 8 faculties, 3
institutions, 5 schools of higher education, 7 vocational schools of higher education and 16 research
and application centers, and 7 different campuses in which education maintains.
Kırşehir Ahi Evran University, by the President of the Republic of Turkey Mr. Recep Tayyip Erdogan
made a statement on 18.01.2016, is selected as one of five pilot universities in the field of agriculture
and geothermal by within the scope of “Regional Development Focused Mission Differentiation and
Specialization Project”. Ahi Evran University is also the first and only university to be awarded the ISO
9001: 2015 Quality Management System Certificate by successfully completing the ISO 9001: 2015
Quality Management Standard External Audit Process with all its units.
The projects of our university are
• Geothermal Welding and Transmission to Project Fields
• Clustering Project in Thermal Sera
• Roughage Production Project
• Walnut-Focused Development and Development Project
• Geothermal Rehabilitation Center Project
• Sportsman Health Research, Application and Thermal Rehabilitation Center Project
• Training and Promotion Project of Pilot University Projects.
I would like to share some historical information about Kırşehir. Kırşehir is a region with a number of
prominent cultures which have lived throughout the history and it has the traces of Hititian, Phrygian,
Lydian, Cappadocian, Roman, Seldjukian and Ottoman civilizations. Also it is the homeland of Aşıkpaşa
who wrote the first Turkish masterpiece, Cacabey who carried out astronomical studies by examining
the stars reflecting on water inside a well in the madrasa he founded, Ahi Evran-ı Veli who organized
merchants and craftsmen, Yunus Emre, Ahmet Gülşehri, Süleyman Türkmani, Şeyh Edabali and Mesut
Gülşehri who contributed in literature and culture.
The fundamental duty of universities is to produce information. The means of these are conferences,
symposiums, workshops, etc. In this sense, we will discuss problems related to mathematics and reach
to solutions in this conference.
The purpose of this conference is to bring together experts and young analysts from all over the world
working in different fields of mathematics and its applications to present their researches, exchange new
ideas, discuss challenging issues, foster future collaborations and interact with each other.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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This conference allows the participation of many prominent experts from different countries who will
present works on different fields of mathematics, especially fixed point theory, approximation theory,
nonlinear analysis, variational analysis, optimization, summability theory, sequence spaces, dynamical
systems and their applications, and also algebra, geometry.
It bring together more than 130 participants from countries of different part of the world for example
Algeria, Ajarian, Azerbaijan, Egypt, Congo, Yemen, Korea, China, India, Iran, Sudan, Morocco, Saudi
Arabia, Tunisia, Ghana, Turkey, Uzbekistan, United States of America, Jordan, out of which 124 are
contributing to the meeting with oral and 3 with poster presentations, including five plenary talks.
We also thank pleanery speaker distinguished Prof. Mohammad MURSALEEN, distinguished Prof.
Zuhair NASHED, distinguished Prof. Jong Kyu KIM, distinguished Prof. Qamrul Hasan ANSARI and
distinguished Prof. Bayram ŞAHİN for contribution to the our symposium.
We hope to promote collaborative and networking opportunities among senior scholars and graduate
students in order to advance new perspectives. The additional emphasis at ICAA-2018 is to put
importance on applications in related areas, as well as other science, such as natural science,
economics, computer science and various engineering sciences.
The papers presented in this conference will be considered in the journals listed on the conference
websites and below:
• Journal of Nonlinear and Convex Analysis (SCI-Exp),
• Carpathian Journal of Mathematics (SCI-Exp),
• Bulletin of Mathematical Analysis and Applications (E-SCI),
• Journal of Inequalities and Special Functions (E-SCI.),
• Creative Mathematics and Informatics,
• Istanbul Commerce University Journal of Science,
• Nonlinear Functional Analysis and Applications (SCOPUS).
This booklet contains the titles and abstracts of almost all invited and contributed talks at the 4th
International Conference on Analysis and Its Applications. Only some abstracts were not available
at the time of printing the booklet. They will be made available on the conference website
www.icaa2018.org when the organizers receive them. All talks will take place in Faculty of Arts and
Sciences in Ahi Evran University, Bağbaşı Campus, Kırşehir/Turkey.
We wish everyone a fruitful conference and pleasant memories in Kırşehir, Turkey.
Prof. Vatan KARAKAYA
On Behalf of Organizing Committee
Chairman
(Rector of Ahi Evran University)
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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Analysis is one of the most important topics in mathematics and has been a focus of attention
of all great mathematicians. There are many areas comes under this topic. However, this conference
mainly devoted to some selected topics from analysis, mainly, Theory of Summability and
Approximation, Fixed Point Theory, Fourier Analysis, Wavelet and Harmonic Analysis, Variational
Analysis, Convex Analysis and Optimization, Geometry of Banach Spaces, Sequence Spaces and
Matrix Transformations. During the last half century, nonlinear and variational analysis have been
developed very rapidly because of their numerous applications to optimization, control theory,
economics, engineering, management, medical sciences and other disciplines. On the other hand, the
modern summability theory plays a very important role in linking theory of sequence spaces and matrix
transformations with measures of noncompactness. Measures of noncompactness are widely used tools
in fixed point theory, differential equations, functional equations, integral and integro-differential
equations, optimization, etc. In the recent years, measures of noncompactness have also been used in
defining geometric properties of Banach spaces as well as in characterizing compact operators between
sequence spaces. We expect the participation of many prominent experts from different countries who
will present their current research work and will also mention some hot topics for further research.
Prof. Qamrul Hasan ANSARI
It was a great moment of excitement when Prof. (Dr.) Vatan Karakaya, Rector, Ahi Evran
University, discussed with me the matter of organizing the “International Conference on Analysis and Its
Applications (ICAA-2018)” at Ahi Evran University, Kırşehir. Now it is a matter of great pleasure that the
matter of holding this conference is finally materialized. This conference is in the sequel of the first one
which was held during December 19-21, 2015 (ICAA-2015) in Aligarh Muslim University, India, the
second one which was held during July12-15, 2016 (ICAA-2016) in Ahi Evran University, Kırşehir and
third one was held during November 20-22, 2017 (ICAA-2017) in Aligarh Muslim University. Being one
of the Co-Chairmen of the conference, I feel privileged and delighted to welcome all delegates, eminent
mathematicians, speakers and young researchers in this international event. It is expected that the
delegates and the participants will be benefitted by the experience of this conference and the legacy of
knowledge dissemination will be continued.I wish all of you to have a nice and enjoyable participation in
the conference. Prof. Mohammad MURSALEEN
We are deeply honored to be the host of this prestigious International Conference on Analysis
and Its Applications (ICAA-2018). On behalf of organizing committee, I would like to extend my heartiest
welcome to all the invited speakers, presenters and participants and to thank all of you for your
support.At this conference we had the opportunity to meet and host many valuable scientists from
different countries of the world. We have received more than 120 papers for presenting. Corresponding
participants have joined us in presenting their ideas and achievements, as well as participated in the
International Conference on Analysis and Its Applications (ICAA-2018)”. We hope that, this conference
will promote the sharing of experiences and strengthen collaborations among the participants doing and
applying mathematics. My deepest appreciation goes for his valuable support in organizing the
conference to Prof. KARAKAYA, who is the Chairman of the ICAA-2018 and Rector of the Kırşehir Ahi
Evran University. Also, I would like to thank the honorable scientists Prof. Ansari, Prof. Kim, Prof.
Mursaleen, Prof. Nashed and Prof. Şahin for accepting our invitation to join the conference as a invited
speaker. Finally, I would like to thank the presenters, participants, the ICAA-2018 working committee for
their hard work and decisiveness, and any who have directly or indirectly contributed to make ICAA-
2018 a success.
Prof. Necip ŞİMŞEK
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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Scientific Committee
A. Ioan RUS (Romania) Manaf MANAFLI (Turkey)
Abdul Rahim KHAN (Saudi Arabia) Mehmet Ali SARIGÖL (Turkey)
Akhtam DZHALİLOV (Uzbekistan) Mehmet Emin ÖZDEMİR (Turkey)
Aldona DUTKIEWICZ (Poland) Metin BAŞARIR (Turkey)
Ali AKBULUT (Turkey) Mikail ET (Turkey)
Ayhan ŞERBETÇİ (Turkey) Mohamed Amine KHAMSI (USA)
Bayram ŞAHİN (Turkey) Mohammad MURSALEEN (India)
Billy E. RHOADES (USA) Mohammad IMDAD (India)
Brailey SIMS (Australia) Murat KİRİŞÇİ (Turkey)
Bünyamin AYDIN (Turkey) Murat ÖZDEMİR (Turkey)
Calogero VETRO (Italy) Murat SARI (Turkey)
Cemil TUNÇ (Turkey) Müzeyyen ERTÜRK (Turkey)
Davide LA TORRE (UAE, Italy) Naim L. BRAHA (Kosova)
Daya Ram SAHU (India) Narin PETROT (Thailand)
Doğan KAYA (Turkey) Nazim B. KERİMOV (Turkey)
Duran TÜRKOĞLU (Turkey) Necip ŞİMŞEK (Turkey)
Ekrem SAVAŞ (Turkey) Nour El Houda BOUZARA (Algeria)
Emrah Evren KARA (Turkey) P. VEERAMANI (India)
Fahreddin ABDULLAYEV (Turkey) Poom KUMAM (Thailand)
Faik GÜRSOY (Turkey) Pratulananda DAS (India)
Fatih NURAY (Turkey) QamrulHasan ANSARI (India)
Franco GIANNESSI (Italy) Rais AHMAD (India)
Gradimir V. MILOVANOVIC (Serbia) Ravi P. AGARWAL (USA)
Hamdullah ŞEVLİ (Turkey) Rıfat ÇOLAK (Turkey)
Hanlar REŞİDOĞLU (Turkey) Richard F. PATTERSON (USA)
Harun POLAT (Turkey) Sebaheddin ŞEVGİN (Turkey)
Henryk HUDZIK (Poland) Seyit TEMİR (Turkey)
Heybetkulu S MUSTAFAYEV (Turkey) Sezgin AKBULUT (Turkey)
Hong-Kun XU (China) Suheil A. KHOURY (UAE)
Hüseyin ÇAKALLI (Turkey) Ştefan MARUŞTER (Romania)
İlham ALİYEV (Turkey) Themistocles M. RASSIAS (Greece)
İsmail EKİNCİOĞLU (Turkey) Tomás Domínguez BENAVIDES (Spain)
İsmail KÜÇÜK (Turkey) Vagif GULİYEV (Azerbaijan)
Jen-Chih YAO (Taiwan) Vasile BERINDE (Romania)
Jesús Garcia-FALSET (Spain) Viktor I. BURENKOV (England)
Johannes J. A. EKSTEEN (South Africa) Vishnu Narayan MISHRA (India)
Johnson O. OLALERU (Nigeria) W.C. WONG (Taiwan)
Jong Kyu KIM ( Korea) Wataru TAKAHASHI (Japan)
Józef BANAS (Poland) William Art KIRK (USA)
Kadri DOĞAN (Turkey) Yılmaz ALTUN (Turkey)
Kaleem Raza KAZMI (India) Yunus ATALAN (Turkey)
Kazimierz GOEBEL (Poland) Zuhair NASHED (USA)
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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Organizing Committee
Prof. Dr. Vatan KARAKAYA, Chairman, Yildiz Technical University, Istanbul, Turkey
Prof. Dr. Mohammad MURSALEEN, Co-Chair, Aligarh Muslim University, Aligarh, India
Prof. Dr. Necip ŞİMŞEK, Co-Chair, Istanbul Commerce University, Turkey
Prof. Dr. Qamrul Hasan ANSARI, Co-Chair, Aligarh Muslim University, Aligarh, India
Assoc. Prof. Dr. Faik GÜRSOY, Adıyaman University, Adıyaman, Turkey
Assoc. Prof. Dr. Handan KÖSE, Ahi Evran University, Kirsehir, Turkey
Assoc. Prof. Dr. Müzeyyen ERTÜRK, Adıyaman University, Adıyaman, Turkey
Assist. Prof. Dr. Javid ALI, Aligarh Muslim University, Aligarh, India
Assist. Prof. Dr. Kadri DOĞAN, Artvin Çoruh University, Artvin, Turkey
Assist. Prof. Dr. Nil MANSUROĞLU, Ahi Evran University, Kirsehir, Turkey
Assist. Prof. Nour El Houda BOUZARA, University of Sci. and Tech., Algeria
Assist. Prof. Dr. Yunus ATALAN, Aksaray University, Turkey
Res. Assist. Arife Aysun KARAASLAN, Işık University, Istanbul, Turkey
Res. Assist. Derya SEKMAN, Ahi Evran University, Kirsehir, Turkey
Res. Assist. Emirhan HACIOĞLU, Yildiz Technical University, Istanbul, Turkey
Phd. Stud. Muhammed KNEFATIi, Yildiz Technical University, Istanbul, Turkey
Msc. Stud. Zhamile ASKEROVA, Istanbul Commerce University, Turkey
Phd. Stud. Reyhan TELLİOĞLU, Istanbul Commerce University, Turkey
Phd. Stud. Ruken ÇELİK, Istanbul Commerce University, Turkey
TABLE OF CONTENTS
FOREWORDS .................................................................................................................................................... 3
SCIENTIFIC COMMITTEE ................................................................................................................................... 6
ORGANIZING COMMITTEE ................................................................................................................................ 7
PLENARY TALKS ............................................................................................................................................. 13
EKELAND’S VARIATIONAL PRINCIPLE FOR SET-VALUED MAPS........................................................................ 13
Qamrul Hasan ANSARI
SOME RESULTS ON A COMMON ZERO OF A FINITE FAMILY OF ACCRETIVE OPERATORS IN BANACH SPACES ... 14
Jong Kyu KIM
APPLICATIONS OF MEASURES OF NONCOMPACTNESS TO MATRIX TRANSFORMATIONS AND DIFFERENTIAL
AND INTEGRAL EQUATIONS ......................................................................................................................... 15
Mohammad MURSALEEN
PERTURBATION ANALYSIS FOR GENERALIZED INVERSES OF LINEAR OPERATORS AND THE ROLE OF OUTER
INVERSES IN REGULARIZATION OF ILL-POSED PROBLEMS.............................................................................. 16
Zuhair NASHED
RIEMANNIAN MAPS IN KAEHLER GEOMETRY ................................................................................................ 17
Bayram ŞAHİN
CONTRIBUTED TALKS ..................................................................................................................................... 18
ROOTS OF ANALYSIS IN ISLAMIC MATHEMATICS ........................................................................................... 18
Abdulmajid NUSAYR
WAVELET PACKET TRANSFORMATION ASSOCIATED WITH LINEAR CANONICAL HANKEL TRANSFORMATION .. 19
Akhilesh PRASAD, Tanuj KUMAR
CONVERGENCE THEOREMS FOR SOME MAPPINGS IN A TYPE OF PROBABILISTIC NORMED SPACES ................ 20
Arife Aysun KARAASLAN, Vatan KARAKAYA
ON GENERALIZED TRIBONACCI OCTONIONS ................................................................................................. 21
Arzu ÖZKOÇ ÖZTÜRK
SOME INVESTIGATIONS FOR TIME FRACTIONAL KORTEWEG-DE VRIES EQUATION USING THE FINITE
DIFFERENCE METHOD .................................................................................................................................. 22
Asıf YOKUS
SOME NEW RESULTS OF M-ITERATION PROCESS IN HYPERBOLIC SPACES ...................................................... 23
Aynur ŞAHİN
DG SOLUTION OF DIFFUSION-REACTION PROBLEM TO MODEL THE DENSITY OF TUMOR GROWTH DYNAMIC 24
Ayşe SARIAYDIN-FİLİBELİOĞLU
NOTES ON GENERATED Q-POLY GENOCCHI POLYNOMIALS ........................................................................... 25
Burak KURT
THINNESS AND FINE TOPOLOGY WITH RELATIVE CAPACITY ........................................................................... 26
Cihan UNAL, Ismail AYDIN
ON APPLICATIONS OF MULTIDIMENSIONAL AFFINE TRANSFORM IN THE SUPPLY OF MISSING DATA .............. 27
Cuneyt YAZICI, Suleyman CETINKAYA, Hulya KODAL SEVİNDİR
DIMENSION OF PRODUCT OF FOUR HOMOGENEOUS COMPONENTS IN FREE LIE ALGEBRAS .......................... 28
Derya KARATAŞ, Nil MANSUROĞLU
ON THE F-CONTRACTION OF THE DARBO THEOREM GENERALIZED BY FUNCTION CLASSES ............................ 29
Derya SEKMAN, Vatan KARAKAYA
ISHIKAWA ITERATION PROCESS AS CONTROL SYSTEMS AND CHAOTIC DISCRETE DYNAMICAL SYSTEMS ......... 30
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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Derya SEKMAN, Vatan KARAKAYA
SYMMETRY ANALYSIS AND CONSERVATION LAWS OF THE BOUNDARY VALUE PROBLEMS FOR TIME-
FRACTIONAL GENERALIZED BURGERS' DIFFERENTIAL EQUATION .................................................................. 31
Dogan KAYA, Gulistan ISKANDAROVA
SOME REMARKS RELATED TO CONTRACTION MAPPINGS ON F-METRIC SPACES ............................................ 32
Emrah Evren KARA, Merve İLKHAN
SOME NEW INEQUALITIES AND HERMITE-HADAMARD-FEJER INEQUALITY VIA NON-NEWTONIAN CALCULUS 33
Erdal ÜNLÜYOL, Yeter ERDAŞ
ASYMPTOTICALLY 𝑰𝟐-INVARIANT EQUIVALENCE OF DOUBLE SEQUENCES AND SOME PROPERTIES ................ 34
Erdinç DÜNDAR, Uğur ULUSU and Fatih NURAY
HELICOIDAL HYPERSURFACES OF DINI-TYPE IN THE FOUR DIMENSIONAL MINKOWSKI SPACE ........................ 35
Erhan GÜLER, Ömer KiŞi
TORUS HYPERSURFACE IN 4-SPACE .............................................................................................................. 36
Erhan GÜLER, Ömer KiŞi
ON QUASI-LACUNARY INVARIANT CONVERGENCE OF SEQUENCES OF SETS ................................................... 37
Esra GÜLLE, Uğur ULUSU
SOME FIXED POINT RESULTS FOR A NEW THREE STEPS ITERATION PROCESS IN BANACH SPACES: A REVISIT ... 38
Faik GÜRSOY, Müzeyyen ERTÜRK, Vatan KARAKAYA
AN APPLICATION OF THREE DIMENSIONAL CELLULAR AUTOMATA WITH PBC .............................................. 39
Ferhat SAH
AN APPLICATION OF ONE DIMENSIONAL CELLULAR AUTOMATA UNDER INTERMEDIATE BOUNDARY
CONDITION ................................................................................................................................................. 40
Ferhat SAH
NUMERICAL APPROACH BASED ON LAGRANGE POLYNOMIALS FOR SOLVING FREDHOLM INTEGRAL
EQUATIONS ................................................................................................................................................. 41
Fernane KHAIREDDINE
SOME BOUNDS OF THE FINITE HILBERT TRANSFORM AND APPLICATIONS IN NUMERICAL INTEGRATION ....... 42
Fuat USTA
P-3-PRIME IDEALS IN NEAR RINGS ................................................................................................................ 43
Funda TAŞDEMİR, İsmail TAŞTEKİN
ON INCLUSION THEOREMS FOR ABSOLUTE CESÀRO SUMMABILITY METHODS ............................................. 44
G. Canan HAZAR GÜLEÇ, M. Ali SARIGÖL
ON THE ZERO POINT PROBLEM OF MONOTONE OPERATORS IN CAT(0) SPACES ............................................. 45
G. Zamani ESKANDANI, M. RAEISI
ON MIZOGUCHI-TAKAHASHI'S TYPE SET VALUED (Α-Θ) CONTRACTIONS ......................................................... 46
Gonca DURMAZ, İshak ALTUN, Murat OLGUN ,Hatice ASLAN HANÇER
NOVEL CONTOUR SURFACES TO THE (2+1)-DIMENSIONAL DATE–JIMBO–KASHIWARA–MIWA EQUATION ..... 47
Haci Mehmet BASKONUS
ON THE ROOTS OF AN EVOLUTION EQUATION.............................................................................................. 48
Haci Mehmet BASKONUS
SOME CARISTI TYPE FIXED POINT THEOREMS ON M-METRIC SPACE .............................................................. 49
Hakan SAHIN, İshak ALTUN, Duran TURKOGLU, Hatice ASLAN HANCER
QUASI-HAUSDORFF TRANSFORMATIONS FOR DOUBLE SEQUENCES ............................................................. 50
Hamdullah ŞEVLİ
WEIGHTED COMPOSITION OPERATORS FROM BLOCH-TYPE SPACES INTO BERS-TYPE SPACES ...................... 51
Hamid VAEZI, Mohamad NAGHLISAR
ON SEMICOMMUTATIVE RINGS ................................................................................................................... 52
Handan KOSE
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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SOME OPERATOR INEQUALITIES .................................................................................................................. 53
Havva TİLKİ, Mualla Birgül HUBAN, Mehmet GÜRDAL
EPI EULER CONVERGENCE OF KIND CONVERGENT SETS ................................................................................ 54
Harun POLAT
NEW TOPOLOGY IN 𝜷(𝐼) .............................................................................................................................. 55
Hassan MOUADI, Driss KARIM
INVESTIGATION OF SUBORBİTAL GRAPHS OF THE TYPE Γ0(L, M) = (A BM
CL D) ........................................................ 56
İbrahim GÖKCAN
WEIGHTED STOCHASTIC FIELD EXPONENT LEBESGUE AND SOBOLEV SPACES ................................................ 57
Ismail AYDIN, Cihan UNAL
SOME COMPACTNESS CRITERIONS IN WEIGHTED VARIABLE EXPONENT AMALGAM SPACES .......................... 58
Ismail AYDIN, Cihan UNAL
CONVERGENCE ANALYSIS OF A NEW MODIFIED JUNGCK-THREE-STEP ITERATIVE METHOD IN THE BANACH
SPACES ........................................................................................................................................................ 59
Kadri DOĞAN, Yılmaz ALTUN
CONVERGENCE ANALYSIS OF JUNGCK-MP ITERATIVE METHOD IN THE BANACH SPACES ................................ 60
Kadri DOĞAN, Vatan KARAKAYA
FIXED POINT THEOREMS VIA SIMULATION TYPE FUNCTIONS ........................................................................ 61
Merve İLKHAN
Δ - CONVERGENCE AND STRONG CONVERGENCE IN GENERALIZED CAT (0) SPACES........................................ 62
Mohammad KNEFATI and Vatan KARAKAYA
ON I2-CAUCHY DOUBLE SEQUENCES IN FUZZY NORMED SPACE ..................................................................... 63
Muhammed Recai TÜRKMEN, Erdinç DÜNDAR
LACUNARY STATISTICAL CONVERGENCE IN FUZZY N-NORMED LINEAR SPACES .............................................. 64
Muhammed Recai TÜRKMEN
SOME RESULTS ON 𝝀 − STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES IN FUZZY NORMED SPACE ...... 65
Muhammed Recai TÜRKMEN
LACUNARY I-CONVERGENCE IN FUZZY NORMED SPACES .............................................................................. 66
Muhammed Recai TÜRKMEN
NEW TYPE SOFT SET AND MEDICAL DECION MAKING APPLICATION .............................................................. 67
Murat KİRİŞCİ
REASONABLE MODIFICATIONS UNDER THE B-SPLINE BASIS WITH THE SSPRK54 FOR SOLVING THE BURGERS
EQUATION................................................................................................................................................... 68
Murat SARI, S. Ali-TAHIR
NEW JUNGCK-TYPE ITERATIVE ALGORITHM AND NUMERICAL RECKONING COINCIDENCE POINTS IN CONVEX
METRIC SPACES ........................................................................................................................................... 69
Musa DİKMEN, Faik GÜRSOY
SOME FIXED POINT THEOREMS IN CONE METRIC SPACES OVER BANACH ALGEBRAS...................................... 70
Muttalip ÖZAVŞAR
ON FINITE DIMENSIONAL LEIBNIZ ALGEBRAS ................................................................................................ 71
Mücahit ÖZKAYA, Nil MANSUROĞLU
CONVERGENCE AND STABILITY RESULTS FOR K* ITERATION.......................................................................... 72
Müzeyyen ERTÜRK, Faik GÜRSOY, Vatan KARAKAYA
A STUDY ON LATERAL BASES AND COVERED LATERAL IDEALS OF ORDERED TERNARY SEMİGROUPS ............... 73
M. Yahya ABBASI, Sabahat Ali KHAN and Aakif Fairooze TALEE
APPROXIMATION PROPERTIES OF THE BERNSTEIN-CHLODOWSKY-DURRMEYER OPERATORS ON THE WHOLE
REEL AXIS .................................................................................................................................................... 74
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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Nadire Fulda ODABAŞI, Aydın İZGİ
ON 𝝀𝝂-STATISTICAL CONVERGENCE OF ORDER 𝜶 OF GENERALIZED DIFFERENCE SEQUENCES ........................ 75
Necip ŞİMŞEK, Mikail ET, Vatan KARAKAYA
ON THE DEFORMATION OF SOME BANACH SEQUENCE SPACES ..................................................................... 76
Ruken ÇELİK, Zhamile ASKEROVA, Necip ŞİMŞEK
ON KRAWTCHOUK POLYNOMIALS ................................................................................................................ 77
Nejla ÖZMEN
ASYMPTOTICALLY LACUNARY I-INVARIANT EQUIVALENCE OF SEQUENCES DEFINED BY A MODULUS FUNCTION
................................................................................................................................................................... 78
Nimet P. AKIN, Erdinç DÜNDAR and Uğur ULUSU
ASYMPTOTICALLY I-INVARIANT EQUIVALENCE OF SEQUENCES DEFINED BY A MODULUS FUNCTION ............. 79
Nimet P. AKIN, Erdinç DÜNDAR
ON FINITE DIMENSIONAL LEIBNIZ ALGEBRAS ................................................................................................ 80
Nil MANSUROĞLU, Mücahit ÖZKAYA
A NEW COMPLEX GENERALIZED BERNSTEIN-SCHURER OPERATOR ................................................................ 81
Nursel CETIN
LACUNARY 𝑰𝟐-INVARIANT CONVERGENCE OF DOUBLE SEQUENCES OF FUNCTIONS ON AMENABLE
SEMIGROUP ................................................................................................................................................ 82
Ömer KİŞİ, Erhan GÜLER
A GENERALIZED STATISTICAL CONVERGENCE VIA IDEALS DEFINED BY FOLNER SEQUENCE ON AMENABLE
SEMIGROUPS .............................................................................................................................................. 83
Ömer KİŞİ, Erhan GÜLER
ON THE NEW SOLUTIONS OF (3+1)-DIMENSIONAL POTENTIAL-YTSF EQUATION BY 𝒕𝒂𝒏𝑭𝝃𝟐-EXPANSION
METHOD ..................................................................................................................................................... 84
Ozlem KIRCI, Hasan BULUT
CONVERGENCE OF THE INVERSE CONTINUOUS WAVELET TRANSFORM IN WEIGHTED VARIABLE EXPONENT
AMALGAM SPACES ...................................................................................................................................... 85
Öznur KULAK, İsmail AYDIN
A NEW OPERATOR IDEAL ON BLOCK SEQUENCE SPACES ............................................................................... 86
Pınar ZENGİN ALP, Emrah Evren KARA
ON BICOMPLEX JACOBSTHAL-LUCAS NUMBERS ........................................................................................... 87
Serpil HALICI, Sevim ASLAN
ALGEBRA OF CONVERGENCE SET SEQUENCE ................................................................................................ 88
Sibel ÖZTÜRK and Harun POLAT
RESULTS ON A CLASS OF HARMONIC UNIVALENT FUNCTIONS INVOLVING A NEW DIFFERENTIAL OPERATOR . 89
Sibel YALÇIN TOKGÖZ, Şahsene ALTINKAYA
CERTAIN CONVEX HARMONIC FUNCTIONS DEFINED BY SUBORDINATION ..................................................... 90
Sibel YALÇIN TOKGÖZ, Şahsene ALTINKAYA
CERTAIN SUBCLASSES OF HARMONIC UNIVALENT FUNCTIONS ASSOCIATED WITH A MULTIPLIER LINEAR
OPERATOR .................................................................................................................................................. 91
Sibel YALÇIN TOKGÖZ, Şahsene ALTINKAYA
AN H-DEFORMATION OF SYMPLECTIC (1+2)-SUPERSPACE VIA A CONTRACTION ............................................. 92
Sultan Abaci CELIK, Canan AYDEMIR
ON A SUBCLASS OF BI-UNIVALENT FUNCTIONS WITH THE FABER POLYNOMIAL EXPANSIONS ........................ 93
Şahsene ALTINKAYA, Sibel YALÇIN
CHEBYSHEV POLYNOMIAL COEFFICIENT RESULTS ON A SUBCLASS OF ANALYTIC AND BI-UNIVALENT
FUNCTIONS INVOLVING QUASI-SUBORDINATION ......................................................................................... 94
Şahsene ALTINKAYA, Sibel YALÇIN
ON THE BOUNDS OF GENERAL SUBCLASSES OF ANALYTIC AND BI-UNIVALENT FUNCTIONS ASSOCIATED WITH
SUBORDINATION ......................................................................................................................................... 95
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
12
Şahsene ALTINKAYA, Sibel YALÇIN
STATISTICAL CONVERGENCE OF MINIMA AND MINIMIZERS OF SEQUENCES OF FUNCTIONS .......................... 96
Şükrü TORTOP, Yurdal SEVER and ÖZER TALO
ON THE Σ-STABLE FAMILIES .......................................................................................................................... 97
Taner BÜYÜKKÖROĞLU, Özlem ESEN, Vakıf CAFER
ON SOME ASYMPTOTICALLY EQUIVALENCE TYPES FOR DOUBLE SEQUENCES AND RELATIONS AMONG THEM
.................................................................................................................................................................. .98
Uğur ULUSU, Erdinç DÜNDAR
STATISTICAL LACUNARY INVARIANT SUMMABILITY OF DOUBLE SEQUENCES ................................................. 99
Uğur ULUSU, Esra GÜLLE
REDUCTION OF NAVIER-STOKES EQUATION TO A LINEAR EQUATION .......................................................... 100
Waleed KHEDR
EXTENDED KRYLOV METHOD FOR THE NUMERICAL RESOLUTION OF A LARGE SCALE DIFFERENTIAL SYMMETRIC
STEIN EQUATIONS ..................................................................................................................................... 101
Yaprak DERICIOGLU and Muhammet KURULAY
ON A NEW ESCAPE CRITERIONS FOR COMPLEX POLYNOMIALS USING FIXED POINT ITERATION METHOD AND S-
CONVEXITY ................................................................................................................................................ 102
Yunus ATALAN, Vatan KARAKAYA
A NEW ITERATION METHOD AND SOME FIXED POINT RESULTS ................................................................... 103
Yunus ATALAN
ON EXISTENCE AND UNIQUINESS OF SOME CLASS NONLINEAR EIGENVALUE PROBLEM ............................... 104
Yusuf ZEREN and Lutfi AKIN
OBTAINING THE FINITE DIFFERENCE APPROXIMATION OF TRANSMISSION CONDITIONS OF DEFORMATION
PROBLEM FOR MULTILAYERED MATERIALS ................................................................................................ 105
Zahir MURADOGLU, Vildan YAZICI, Tatsiana URBANOVICH
POSTER SESSION.......................................................................................................................................... 106
SUMS OF ELEMENT ORDERS IN FINITE GROUPS .......................................................................................... 106
Ayşe Nur KÖKSAL, Nil MANSUROĞLU
APPROXIMATION BY GENERALIZED COMPLEX SZÁSZ-MIRAKYAN OPERATORS IN COMPACT DISK................. 107
Döne KARAHAN, Sevilay K. SERENBAY, Aydın İZGİ
ON APPROXIMATION BY GENERALIZED BERNSTEIN-KANTOROVICH OPERATORS OF TWOVARIABLE ............ 108
Döne KARAHAN, Aydın İZGİ
NON PRESENTING PARTICIPANTS ................................................................................................................. 109
INDEX ........................................................................................................................................................... 110
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
13
PLENARY TALKS
EKELAND’S VARIATIONAL PRINCIPLE FOR SET-VALUED MAPS
Qamrul Hasan ANSARI
Department of Mathematics, Aligarh Muslim University, Aligarh, India
qhansari@gmail.com
Abstract: The Ekeland variational principle (in short, EVP) is one the most applicable results from
nonlinear analysis and used as a tool to study the problems from fixed point theory, optimization,
optimal control theory, game theory, nonlinear equations, dynamical systems, etc. It was established
by Ekeland in 1972 and provides the existence of an approximate minimizer of a bounded below and
lower semicontinuous function defined on a complete metric space. Later, it is found that several
well-known results, namely, Caristi-Kirk fixed point theorem, Takahashi's minimization theorem,
Petal theorem and the Danes drop theorem, from nonlinear analysis are equivalent to the Ekeland's
variational principle. In 1981, Sullivan established that the conditions of EVP on a metric space (X,d)
imply the completeness of the metric space (X,d). In the last two decades, EVP has been generalized
in different directions, namely, it has been extended for bifunctions, called equilibrium version of
Ekeland’s variational principle; for vector-valued functions, for set-valued maps, etc.
The main aim of this talk is to discuss Ekeland varitaional principle for real-valued functions, for
vector-valued functions and for set-valued functions. We shall give some of our recent results on this
topic.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
14
SOME RESULTS ON A COMMON ZERO OF A FINITE FAMILY OF ACCRETIVE
OPERATORS IN BANACH SPACES
Jong Kyu KIM
1Department of Mathematics Education, Kyungnam university,Changwon, Gyeongnam , 51767, Korea,
jongkyuk@kyungnam.ac.kr
Abstract: In this talk, we introduce some new iterative methods to find a common zero of a finite
family of nonlinear operators in Banach spaces. We first introduce some strong convergence
theorems for the problem of finding a common zero of a finite family of monotone operators and also,
we give some problems of finding a common fixed point of a finite family of nonexpansive mappings
in Hilbert spaces by shrinking projection method. Next, we deal with strong convergence theorems
for finding a common zero of a finite family of accretive operators in Banach spaces with the weak
control conditions.
Keywords: Common zeros, monotone operators, accretive operators, shrinking projection method,
resolvent method, Halpern`s method.
References:
[1] J.K. Kim and T.M. Tuyen, Alternating resolvent algorithms for finding a common zero of two
accretive operator in Banach spaces, Jour. Korean Math. Soc. 54(6)(2017), 1905-1926.
[2] J.K. Kim and T.M. Tuyen, New iterative methods for finding a common zero of a finite family
of monotone operators in Hilbert spaces, Bull
Korean Math. Soc. 54(4)(2017), 1347-1359.
[3] J.K. Kim and T.M. Tuyen, Approximation common zero of two
accretive operators in Banach spaces, Applied Mathematics and Comput., 283(2016), 265-281.
[4] J.K. Kim and T.M. Tuyen, On the some regularization methods for
common fixed point of a finite family of nonexpansive mappings, Journal of Nonlinear and Convex
Analysis, Vol.17(1) (2016), 99-104.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
15
APPLICATIONS OF MEASURES OF NONCOMPACTNESS TO MATRIX
TRANSFORMATIONS AND DIFFERENTIAL AND INTEGRAL EQUATIONS
Mohammad MURSALEEN
Department of Mathematics, Aligarh Muslim University, Aligarh/INDIA
mursaleenm@gmail.com
Abstract: In this talk, we present a brief survey of theory and applications of measures of
noncompactness. The classical measures of noncompactness are discussed and their properties
are compared. The approaches for constructing measure of noncompactness in a general metric or
linear space are described, along with the classical results for existence of fixed point for condensing
operators. Also several generalization of classical results are mentioned and their applications in
various problems of analysis such as linear equation, di§erential equations, integral equations and
common solutions of equations are discussed. The most effective way in the characterization of
compact operators between the Banach spaces is applying the Hausdorff measure of
noncompactness. In this talk, we present some identities or estimates for the operator norms and
the Hausdorff measures of noncompactness of certain operators given by infinite matrices that map
an arbitrary BK-space into the sequence spaces 𝑐0, 𝑐 , 𝑙∞ and 𝑙1.Many linear compact operators may
be represented as matrix operators in sequence spaces or integral operators in function spaces [1].
Recently the measures of noncompactness are applied in solving infinite system of differential
equations [3] and integral equations in sequence spaces [2].
Keywords: Measures of noncompactness, differential equations, sequencespaces.
References:
[1] J. Banas and M. Mursaleen, Sequence Spaces and Measures of Noncompactness with
Applications to Differential and Integral Equations, Springer, 2014.
[2] Das, B. Hazarika, R. Arab and M. Mursaleen, Solvability of the infinite system of integral
equations in two variables in the sequence spaces c_0 and l_1, Jour. Comput. Appl. Math., 326
(2017) 183-192.
[3] M. Mursaleen and S.M.H Rizvi, Solvability of the infinite system of second order differential
equations in c_0 and l_1 by Meir-Keeler condensing operator. Proc. Amer.Math.Soc., 144 (10) (2016)
4279-4289.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
16
PERTURBATION ANALYSIS FOR GENERALIZED INVERSES OF LINEAR
OPERATORS AND THE ROLE OF OUTER INVERSES IN REGULARIZATION
OF ILL-POSED PROBLEMS
Zuhair NASHED
Department of Mathematics, University of Central Florida, Orlando, Florida, USA
Abstract: Inverse Problems deal with determining for a given input-output system an input that
produces an observed output, or determining an input that produces an output that is as close as
possible to a desired output, often in the presence of noise. Most inverse problems are ill-posed, so
their resolution requires some methods of regularization.
Signal Analysis/Processing deals with digital representations of signals and their analog
reconstructions from digital representation.Sampling expansions, filters, reproducing kernel Hilbert
spaces, various function spaces, and techniques of functional analysis, computational and applied
harmonic analysis play pivotal role in this area.
This talk will highlight some land marks in these two areas and discuss some common threads
between them. We will show that function spaces, in particular reproducing kernel Hilbert spaces,
play a magical role in bothill-posed inverse problems and sampling expansion theorems.
The year 2016 marks the 110th birthday of the great Russian mathematician Andrey Nikoayevich
Tikhonov (October 30, 1906 - October 7, 1993) and the 100th birthday of the great American
mathematician Claude Elwood Shannon (April 30, 1916 - February 24, 2001). We celebrate their
memory and seminal contributions to regularization theory of ill-posed problems, and sampling
expansions and communication theory, respectively.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
17
RIEMANNIAN MAPS IN KAEHLER GEOMETRY
Bayram ŞAHİN
Ege University, Department of Mathematics, 35100, Izmir, Turkey.
bayram.sahin@ege.edu.tr
Abstract: Riemannian maps were introduced by Fischer in [4] as a generalization of isometric
immersions and Riemannian submersions. Later such maps have been considered from (to) Kaehler
manifolds ( see [5] for detais) as generalizations of holomorphic submanifolds, totally real
submanifolds [6], CR-submanifolds [1], generic submanifolds [2], slant submanifolds[3], holomorphic
submersions, anti-invariant Riemannian submersions, semi-invariant Riemannian submersions,
generic submersions, slant submersions [5]. In this talk, we survey recent results on the geometry
of Riemannian maps from (to) Kaehler manifolds and give several examples.
References:
[1] A.Bejancu, Geometry of CR-submanifolds, Kluwer, 1986.
[2] B.Y.Chen, Geometry of submanifolds and Its applications, Science University of Tokyo, 1981.
[3] B.Y.Chen, Geometry of Slant Submanifolds, Katholike University, Leuven, 1990.
[4] A.E.Fischer, Riemannian Maps Between Riemannian Manifolds, Contemporary Mathematics,
132, 1992.
[5] B.Şahin, Riemannian Submersions, Riemannian Maps in Hermitian Geometry and Their
Applications, Elsevier, 2016.
[6] K. Yano,M.Kon, Structures on Manifolds, World Scientific, 1984.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
18
Contributed Talks
ROOTS OF ANALYSIS IN ISLAMIC MATHEMATICS
Abdulmajid NUSAYR
Professor Emeritus
Jordan University of Science and Technology
Abstract: Mathematics like other fields of knowledge is cumulative. The roots of mathematical
analysis may be traced to the earlier mathematical activities as may be understood in Egyptian,
Mesopotamian and Greek mathematics. However, these aspects were none direct and ambiguous.
When we come to Islamic era we find these roots are clear and applicable. We shed light on three
fields where Islamic mathematicians treated analysis loud and clear. We look into the works of Al-
Hasan (Al-hazen) ibn Al-Haitham and his famous problem; arithmatization of al-Jabr by al-Karji and
the use of first derivative to find extremum values by Abu- Muzaffar Altusi.
جذور التحليل الرياضي في الرياضيات اإلسالمية
عبد المجيد نصير
أستاذ الشرف
جامعة العلوم والتكنولوجيا األردنية
الرياضية في رياضيات الرياضيات معرفة تراكمية، شأنها كغيرها من المعارف. ويمكن تتبع جذور التحليل الرياضي إلى بدايات النشاطات
المصريين وما بين النهرين واإلغريق. لكن هذه المالمح كانت غير مباشرة وغامضة. وعندما نأتي إلى الرياضيات اإلسالمية نجد هذه الجذور
في مسألة واضحة ومطبقة. في هذا البحث نلقي الضوء على ثالثة مجاالت تعامل الرياضيون اإلسالميون مع التحليل بقوة ووضوح. سننظر
الحسن )الحسن بن الهيثم( الشهيرة، وحسبنة الجبر لمحمد الكرجي، وإيجاد القيم القصوى باستعمال المشتقة األولى ألبي المظفر الطوسي.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
19
WAVELET PACKET TRANSFORMATION ASSOCIATED WITH LINEAR
CANONICAL HANKEL TRANSFORMATION
Akhilesh PRASAD, Tanuj KUMAR
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines),Dhanbad.
826004, Jharkhand, India.
apr_bhu@yahoo.com
tanujdimri067@gmail.com
Abstract: The main goal of this paper is to construct wavelet packet transformation in terms of linear
canonical Hankel transformation and discuss some of its basic properties. An inversion formula for
linear canonical wavelet packet transformation is also obtained. Some examples are also discussed.
Keywords: Linear canonical Hankel wavelet, Convolution, Translation.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
20
CONVERGENCE THEOREMS FOR SOME MAPPINGS IN A TYPE OF
PROBABILISTIC NORMED SPACES
Arife Aysun KARAASLAN1, Vatan KARAKAYA2
1Department of Mathematics, Işık University, İstanbul/TURKEY
karaaslan.aysun@gmail.com
2Department of Mathematical Engineering, Yıldız Technical University, İstanbul/TURKEY
vkkaya@yahoo.com
Abstract: In this presentation, we obtain the definition of probabilistic demicontractive mapping in a
S-probabilistic normed space. Also, probabilistic convergence theorems for these mappings are
proved.
Keywords: Probabilistic normed space, demicontractive mapping, fixed point.
Acknowledgement: The first author was supported by TÜBİTAK- The Scientific and Technological
Research Council of Turkey.
References:
[1] Xu Y., Guan J., Su Y., Weak and Strong Convergence Theorems of Fixed Points for
Nonexpansive Mappings and Strongly Pseudocontractive Mappings in a New Class of Probabilistic
Normed Spaces, Fixed Point Theory and Applications, 2015.
[2] Alsina C., Schwizer B., Sklar A., On the Definition of Probabilistic Normed Space. Aequ.
,Math., 46, 91-98 (1993).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
21
ON GENERALIZED TRIBONACCI OCTONIONS
Arzu ÖZKOÇ ÖZTÜRK
Düzce University, Faculty of Art and Science, Department of Mathematics, Düzce, Turkey
arzuozkoc@duzce.edu.tr
Abstract: In this work, we investigate the properties of generalized tribonacci octonions over the
octonion algebra. After presenting generating functions and Binet formulas, we obtain some
properties of these types of octonions.
Keywords: Binet formulas, octonion, generating functions, generalized tribonacci sequence.
References:
[1] Koshy T., Fibonacci and Lucas Numbers with Applications, Wiley Intersection Pub., New York,
2001.
[2] Cerda-Morales G., "The Third order Jacobsthal Octonions: Some Combinatorial Properties.’’ https://arxiv.org/abs/1710.00602.pdf.
[3] Akkuş I. and Kizilaslan G., "On Some Properties of Tribonacci Quaternions.’’
https://arxiv.org/pdf/1708.05367.pdf.
[4] Çimen C.B. and Ipek A., "On Jacobsthal and Jacobsthal-Lucas Octonions. ’’ Mediterranean
Journal of Mathematics, 14:37 (2017), 1–13.
[5] Cerda-Morales G., "On a Generalization for Tribonacci Quaternions.’’ Mediterranean Journal of
Mathematics, 14:239(2017)1-12.
[6] Catarino P., "The modified Pell and the modified k-Pell quaternions and octonions. " Adv. Appl.
Clifford Algebras, 26 (2016), 577–590.
[7] Pethe S., "Some Identities for Tribonacci Sequences." The Fibonacci Quarterly, 26(2) (1988),
144–151.
[8] Feinberg M., "Fibonacci-Tribonacci." The Fibonacci Quarterly, 1(3) (1963), 71–74.
[9] Flaut C. and Shpakivskyi V., "On Generalized Fibonacci Quaternions and Fibonacci-Narayana
Quaternions." Adv. Appl. Clifford Algebras, 23(3)(2013), 673-688.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
22
SOME INVESTIGATIONS FOR TIME FRACTIONAL KORTEWEG-DE VRIES
EQUATION USING THE FINITE DIFFERENCE METHOD
Asıf YOKUS
Department of Actuary, Firat University, Elazig, 23200, Turkey
asfyokus@yahool.com
Abstract: In the present work, by using the (1/G')-expansion method and the finite forward difference
method the non-linear time fractional Korteweg-de Vries equation is studied by obtaining the exact
wave solutions of the non-linear time fractional Korteweg-de Vries equation. The index forms for
some derivatives of certain types are considered. It is observed that that the obtained numerical
results approach to the exact solution.
Keywords: Time fractional KdV equation, Finite difference method, Traveling wave solutions
References:
[1] A. Yokus, Solutions of Some Nonlinear Partial Differential Equations and Comparison of Their
Solutions, Ph.D. Thesis, Firat University, (2011).
[2] W. Chen, L. Ye and H. Sun, Fractional di_usion equations by the Kansa method, Comput. Math.
Appl. 59 1614-1620 (2010).
[3] M. Yavuz, N. Ozdemir,New numerical techniques for solving fractional partial differential
equations in conformable sense In Conference on Non-integer Order Calculus and Its Applications,
49-62 Springer, Cham (2017).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
23
SOME NEW RESULTS OF M-ITERATION PROCESS IN HYPERBOLIC
SPACES
Aynur ŞAHİN
Department of Mathematics, Sakarya University, 54050 Sakarya, Turkey
ayuce@sakarya.edu.tr
Abstract: In this study, the strong convergence and weak 2w -stability theorems are proved for M-
iteration process in hyperbolic spaces. Under some suitable conditions, the data dependence result
of this iteration for a class of contractive-type mappings is also established. The results presented
here extend and improve some recent results announced in the current literature.
Keywords: Fixed point, stability, data dependence, hyperbolic space, contractive-type mapping, M-
iteration process.
References:
[1] Ullah, K, Arshad, M: Numerical reckoning fixed points for Suzuki’s generalized nonexpansive
mappings via new iteration process. Filomat 32:1 (2018), 187-196.
[2] Timiş, I: On the weak stability of Picard iteration for some contractive type mappings. Annal.
Uni. Craiova, Math. Comput. Sci. Series, 37:2 (2010), 106-114.
[3] Kohlenbach, U: Some logical metatheorems with applications in functional analysis. Trans.
Amer. Math. Soc. 357 (2004), 89-128.
[4] Osilike, M. O, Udomene, A: Short proofs of stability results for fixed point iteration procedures
for a class of contractive-type mappings. Indian J. Pure Appl. Math. 30:12 (1999), 1229-1234.
[5] Şahin, A, Başarır, M: Convergence and data dependence results of an iteration process in a
hyperbolic space. Filomat 30:3 (2016), 569-582.
[6] Gürsoy, F, Khan, A. R, Ertürk, M, Karakaya, V: Weak 2w -stability and data dependence of
Mann iteration method in Hilbert spaces, RACSAM (2017), doi: 10.1007/s13398-017-0447-y.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
24
DG SOLUTION OF DIFFUSION-REACTION PROBLEM TO MODEL THE
DENSITY OF TUMOR GROWTH DYNAMIC
Ayşe SARIAYDIN-FİLİBELİOĞLU
Scientific and Technological Research Council of Turkey (TÜBİTAK), Tunus Caddesi, No: 80, 06100
Kavaklıdere, Ankara, Turkey,
asariaydin@gmail.com
Abstract: In this work, we numerically solve diffusion-reaction problem modeling the density of the
tumor growth dynamics. We employ a nonlinear heterogeneous diffusion logistic density model [1].
This model assumes that glioma cell invasion throughout the brain is a reaction-diffusion process
and the coefficient of diffusion can vary according to the gray and white matter composition of the
brain at that location. To visualize and investigate numerically the behavior of the evolution of tumor
concentration of the glioma, we propose an efficient discontinuous Galerkin finite elements method
(DGFEM) [2] in space and implicit Euler method in time to solve the equation. Numerical examples
demonstrate effectiveness of the method.
Keywords: diffusion-reaction equation, discontinuous Galerkin, tumor growth.
References:
[1] E. Özuğurlu, A note on the numerical approach for the reaction-diffusion problem to model the
density of the tumor grwoth dynamics. Computers and Mathematics with Applications, 69 (2015),
1504-1517.
[2] B. Rivière, Discontinuous Galerkin methods for solving elliptic and parabolic equations,
Frontiers in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM),
Philadelphia, PA, 2008.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
25
NOTES ON GENERATED q-POLY GENOCCHI POLYNOMIALS
Burak KURT
Department of Mathematics, Akdeniz University,07070 Antalya, Turkey,
burakkurt@akdeniz.edu.tr
Abstract: In recently years, many mathematicians studied q-Bernoulli polynomials, q-Euler
polynomials, q-Genocchi polynomials, poly-Bernoulli, poly-Euler and poly-Genocchi polynomials and
numbers. They investigated and defined some properties of these polynomials. They proved some
symmetric relations for these polynomials. Mahmudov introduced q-Bernoulli polynomials and q-
Genocchi polynomials. Kim et al. introduced poly-Genocchi polynomials. They gave some recurrence
relation for the higher-order poly-Bernoulli polynomials. In this work, we give basic relation for the
generalized q-poly-Genocchi polynomials. We give different relations between the q-poly-Genocchi
polynomials and the Stirling numbers of the second kind.
Keywords: genocchi polynomails and numbers, poly-genocchi polynomials, generating functions.
References:
[1] A. Bayad and Y. Hamahata: “Polylogarithms and poly-Bernoulli polynomials”. Kyushu J. Math.
65 (2011):15-34.
[2] D. Kim and T. Kim: “A note on poly-Bernoulli and higher order poly-Bernoulli polynomials.”
Russian J. of Math. Physics. 22.1 (2015): 26-33.
[3] N. I. Mahmudov: “q-Analogues of the Bernoulli and Genocchi polynomials and the Srivastava-
Pinter addition theorem.” Discrete Dyn. In Natue and Society. Aricle ID:169348. (2012).
[4] H. M. Srivastava: “Some generalization and basic (or q-) extension of the Bernoulli, Euler and
Genocchi Polynomials.” Appl. Math. Inform. Sci. 5 (2011): 390-444.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
26
THINNESS AND FINE TOPOLOGY WITH RELATIVE CAPACITY
Cihan UNAL1, Ismail AYDIN2
1,2Faculty of Arts and Sciences, Department of Mathematics, Sinop University, 57000 Sinop, Turkey,
cihanunal88@gmail.com
iaydin@sinop.edu.tr
Abstract: In this study, we present a thinness with relative capacity for weighted variable exponent
Sobolev spaces. Also, we investigate some properties of finely sets in sense to this thinness.
Moreover, we consider fine topology which is finer than Euclidean topology.
Keywords: Fine topology, Thinness, Relative capacity.
References:
[1] I. Aydın, Weighted variable Sobolev spaces and capacity, J. Funct. Spaces Appl., 2012, Article
ID 132690, (2012)
[2] P. Harjulehto, V. Latvala, Fine topology of variable exponent energy superminimizers, Ann.
Acad. Sci. Fenn.-M., 33, 491-510, (2008)
[3] P. Harjulehto, P. Hästö, M. Koskenoja, Properties of capacities in variable exponent Sobolev
spaces, J. Anal. Appl., 5(2), 71-92, (2007)
[4] J. Heinonen, T. Kilpeläinen, O. Martio, Nonlinear Potential Theory of Degenerate Elliptic
Equations, Oxford University Press, Oxford, (1993)
[5] C. Unal, I. Aydın, On some properties of relative capacity and thinness in weighted variable
exponent Sobolev spaces (Submitted)
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
27
ON APPLICATIONS OF MULTIDIMENSIONAL AFFINE TRANSFORM IN THE
SUPPLY OF MISSING DATA
Cuneyt YAZICI1, Suleyman CETINKAYA2, Hulya KODAL SEVİNDİR3
1,2,3Department of Mathematics Education, Kocaeli University, Umuttepe Campus, İzmit, 41380 Kocaeli,
Turkey,
cuneyt.yazici@kocaeli.edu.tr
suleyman.cetinkaya@kocaeli.edu.tr
hkodal@kocaeli.edu.tr
Abstract: Supply of missing data is one of the image processing applications. Shearlet transform,
which is an important affine transformation, can be used for multivariate data analysis. In this study,
we used shearlet transform in the supply of missing data and we compared the obtained results.
Keywords: supply of missing data, image processing, shearlet, multivariate data.
References:
[1] Kutyniok G., Lim W. Q., “Image Separation Using Wavelets and Shearlets”, Curves and
Surfaces, 6920, 416-430, 2012.
[2] Q., Guo, S., Yu, X., Chen, C., Liu and W.,Wei, “Shearlet-based Image Denoising Using Bivariate
Shrinkage with Intra-band and Opposite Orientation Dependencies”, IEEE Conference Publications,
1, 863–866, 2009.
[3] G. R., Easley and D., Labate, “Image Processing Using Shearlets”, Editors: G., Kutyniok and D.,
Labate Shearlets: Multiscale Analysis for Multivariate Data, Birkhäuser, Boston, 283–325, 2012.
[4] E. J., King, G., Kutyniok and Zhuang X., ““Analysis of Inpainting via Clustered Sparsity and
Microlocal Analysis”, J.Math. Imaging Vis., 48, 205–234, 2014.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
28
DIMENSION OF PRODUCT OF FOUR HOMOGENEOUS COMPONENTS IN
FREE LIE ALGEBRAS
Derya KARATAŞ1, Nil MANSUROĞLU2
1,2Department of Mathematics, Kırşehir Ahi Evran University, 40100 Kırşehir, Turkey,
deryakaratas3@outlook.com
nil.mansuroglu@ahievran.edu.tr
Abstract: Let L be a free Lie algebra of rank ≥ 2 over a field F and let 𝐿𝑛 denote the degree n
homogeneous component of L. In this study, firstly we give that how to calculate the dimension of 𝐿𝑛
and product of two and the dimension of three homogeneous components in free Lie algebra. Then
we show that how to determine the dimension of products of four homogeneous components in free
Lie algebra L.
Keywords: free Lie algebra, homogeneous subspaces, homogeneous components, Witt formula,
free generators.
References:
[1] N. Mansuroğlu, Products of homogeneous subspaces in free Lie algebra, MSc thesis, University
of Manchester, 2010.
[2] N. Mansuroğlu, R. Stöhr, On the dimension of products of homogeneous subspaces in free Lie
algebras, Internat J. Algebra Comput, 23 (2013): 205-213.
[3] R. Stöhr and M. Vaughan-Lee, Products of homogeneous subspaces in free Lie algebras,
Internat J. Algebra Comput, 19 (2009): 699-703.
[4] E. Witt, Treue Darstellungen Liescher Ringe, J. Reine Angew. Math. 177 (1937): 152-160.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
29
ON THE F-CONTRACTION OF THE DARBO THEOREM GENERALIZED BY
FUNCTION CLASSES
Derya SEKMAN1, Vatan KARAKAYA2
1Department of Mathematics, Ahi Evran University, Bagbasi Campus, 40100 Kirsehir, Turkey,
deryasekman@gmail.com
2 Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210
Istanbul, Turkey,
vkkaya@yahoo.com
Abstract: Darbo’s fixed point theory has been studied and generalized with many different concepts.
In this work, we will investigate the behavior and the existence of a fixed point under F-contraction
of the theorem expanded by function classes.
Acknowledgement: This work was supported by the Ahi Evran University Scientific Research
Projects Coordination Unit. Project Number: RKT.A3.17.001.
Keywords: Darbo fixed point theorem, shifting distance function, F-contraction
References:
[1] J. Banas, K. Goebel, Measure of Noncompactness in Banach Spaces, Lecture Notes in Pure
and Applied Mathematics 60, Dekker, New York, 1980.
[2] M. Berzig, Generalization of the Banach Contraction Principle (2013), arXiv:1310.0995
[math.CA].
[3] A. Samadi and M.B. Ghaemi, An Extension of Darbo’s Theorem and Its Application, Abstract
and Applied Analysis 2014 (2014), Article ID 852324, 11 pages.
[4] D. Wardowski, Fixed Points of A New Type of Contractive Mappings In Complete Metric
Spaces, Fixed Point Theory and Appl. 2012, 2012: 94.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
30
ISHIKAWA ITERATION PROCESS AS CONTROL SYSTEMS AND CHAOTIC
DISCRETE DYNAMICAL SYSTEMS
Derya SEKMAN1, Vatan KARAKAYA2
1Department of Mathematics, Ahi Evran University, Bagbasi Campus, 40100 Kirsehir, Turkey,
deryasekman@gmail.com
2 Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210
Istanbul, Turkey,
vkkaya@yahoo.com
Abstract: In this study, chaos structures of dynamics which are formed by applying Ishikawa iteration
processes to function classes with chaotic behavior in discrete dynamic systems have been
investigated. Later, the control mechanisms for chaotic structures have been developed according
to the stable and unstable state of fixed points of this transformation.
Acknowledgement: This work was supported by the Yildiz Technical University Scientific Research
Projects Coordination Unit. Project Number: FDK-2018-3348
Keywords: Discrete dynamical system, chaotical structure, control mechanism, Ishikawa iteration
References:
[1] Berinde, V., Controlling chaotic dynamical systems through fixed point iterative techniques,
"Vasile Alecsandri" University of Bacau Faculty of Sciences Scientific Studies and Research Series
Mathematics and Informatics, Vol. 19 (2009), No. 2, 47-58.
[2] Huang, W., Controlling chaos through growth rate adjustment, Discrete Dyn. Nat.Soc., 7 (3),
191-199, 2002.
[3] Deng, L., Ding, X.P., Ishikawa's Iterations Of Real Lipschitz Functions, Bull. Austral. Math. Soc.,
Vol. 46 (1992): 107-113.
[4] B.E. Rhoades, 'Comments on two fixed point iteration methods', J. Math. Anal. Appl. 56 (1976),
741-750.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
31
SYMMETRY ANALYSIS AND CONSERVATION LAWS OF THE BOUNDARY
VALUE PROBLEMS FOR TIME-FRACTIONAL GENERALIZED BURGERS'
DIFFERENTIAL EQUATION
Dogan KAYA1, Gulistan ISKANDAROVA2
1,2 Department of Mathematics, Istanbul Commerce University, Faculty of Art and Science, 34445 Istanbul,
Turkey,
dkaya36@yahoo.com
gulistan.iskandarova@gmail.com
Abstract: In this work we obtain symmetries of the boundary value problem for fractional nonlinear
generalized Burgers’ differential equation [1, 2]. And find some exact solutions of the nonlinear
generalized Burgers’ differential equation with fractional derivative by using symmetry method [3, 4].
Also we found conservation laws for the nonlinear generalized Burgers’ differential equation.
Keywords: Burgers’ equation, Boundary value problem, Symmetry analysis, conservations laws,
Riemann--Liouville fractional derivative.
References:
[1] Olver P., Applications of Lie groups to differential equations, Springer Science, Germany, 2012.
[2] Ibragimov N., CRC Handbook of Lie Group Analysis of Differential Equations, CRC Press, Boca
Raton, 1994.
[3] Gazizov R.K, Kasatkin A.A., and Lukashchuk S.Y, Continuous transformation groups of
fractional differential equations. Vestn. USATU, 9, 125-135 (2007).
[4] Iskandarova G, and Kaya D, Symmetry solution on fractional equation, IJOCTA, 7(3), 255-259
(2017).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
32
SOME REMARKS RELATED TO CONTRACTION MAPPINGS ON F-METRIC
SPACES
Emrah Evren KARA1, Merve İLKHAN2
1,2Department of Mathematics, Düzce University, Düzce, Turkey,
karaeevren@gmail.com
merveilkhan@gmail.com
Abstract: The purpose of this study is to prove some fixed point theorems with regard to special kind
of self-mappings on a newly introduced generalized metric space.
Keywords: fixed point, contraction mappings, F-metric spaces.
References:
[1] E. Rakotch: A note on contractive mappings, Proc. Amer. Math. Soc. 13, 459-465 (1962)
[2] S. P. Singh and W. Russel, A note on a sequence of contraction mappings, Canad. Math. Bull.
12, 513-516 (1969)
[3] R. Kannan, Some results on fixed points-II, Amer. Math. Monthly 76, 405-408 (1969)
[4] S. Reich: Some remarks concerning contraction mappings, Canad. Math. Bull. 14(1), 121-124
(1971)
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
33
SOME NEW INEQUALITIES AND HERMITE-HADAMARD-FEJER INEQUALITY
VIA NON-NEWTONIAN CALCULUS
Erdal ÜNLÜYOL1, Yeter ERDAŞ2
1,2Department of Mathematics, Ordu University, 52200, Ordu, Turkey,
eunluyol@yahoo.com
yeterrerdass@gmail.com
Abstract: In this study, Hermite-Hadamard-Fejer inequality is expressed and proved in Non-
Newtonian calculus. Then, some new inequalities have been achieved by carrying out Non-
Newtonian calculus of inequality structures that have been generalized using Hermite-Hadamard-
Fejer.
Keywords: Hermite-Hadamard-Fejer inequality, Non-Newtonian calculus.
Acknowledgment: In this study supported by Ordu University Scientific Research number of B-1803
References:
[1] Michael Grosmann and Robert Katz, Non- Newtonian Calculus, Lee Press Pigeon Cove,
Massachusetts (1972).
[2] Agamirza E. Bashirov, Emine Mısırlı Kurpınar, Ali Özyapıcı, Multiplicative calculus and its
applications, J. Math. Anal. Appl. 337, 36–48 (2008).
[3] Uğur Kadak, Newtonyen olmayan analiz ve uygulamaları, Dr. Tezi, Gazi Üniversitesi, (2015).
[4] Erdal Ünlüyol, Seren Salaş, İmdat İşcan, Convex functions and some inequalities in terms of
the Non-Newtonian Calculus April 2017,AIP Conference Proceedings 1833(1):020043,
DOI,10.1063/1.4981691, (2017).
[5] Erdal Ünlüyol, Seren Salaş, İmdat İşcan, A new view of some operators and their properties in
terms of the Non-Newtonian Calculus Topol. Algebra Appl. 2017 (5), 49-54,
https://doi.org/10.1515/taa-2017-0008, (2017).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
34
ASYMPTOTICALLY 𝑰𝟐-INVARIANT EQUIVALENCE OF DOUBLE SEQUENCES
AND SOME PROPERTIES
Erdinç DÜNDAR, Uğur ULUSU and Fatih NURAY
Department of Mathematics, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey,
edundar@aku.edu.tr
ulusu@aku.edu.tr
fnuray@aku.edu.tr
Abstract: In this paper, we give definitions of asymptotically ideal equivalent, asymptotically invariant
equivalent and strongly asymptotically invariant equivalent for double sequences. Also, we give
some properties and examine the existence relationships among these new type equivalence
concepts.
Keywords: asymptotically equivalence, double sequence, ideal convergence, invariant
convergence, ideal invariant equivalence.
References:
[1] E. Dündar, U. Ulusu and F. Nuray, On ideal invariant convergence of double sequences and
some properties, Creat. Math. Inform. 27(2) (2018), 161-169.
[2] B. Hazarika, V. Kumar, On asymptotically double lacunary statistical equivalent sequences in
ideal context, Journal of Inequalities and Applications, 2013:543 (2013), 1-15.
[3] P. Kostyrko, T. Salat and W. Wilczynski, I-Convergence, Real Anal. Exchange, 26(2) (2000),
669-686.
[4] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4) (1993), 755-
762.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
35
HELICOIDAL HYPERSURFACES OF DINI-TYPE IN THE FOUR DIMENSIONAL
MINKOWSKI SPACE
Erhan GÜLER1, Ömer KiŞi2
1,2Bartın University, Faculty of Science, Department of Mathematics, 74100 Bartın, Turkey
eguler@bartin.edu.tr
okisi@bartin.edu.tr
Abstract: In this talk, we consider Italian Mathematician Ulisse Dini’s type helicoidal surfaces in the
three dimensional Euclidean space and then we extend it to the helicoidal hypersurfaces of Dini-type
in the four dimensional Minkowski space. There are three types, depending on the axis of rotation in
Minkowski geometry. Equations for the Gaussian and mean curvature are derived and some
examples of the various types of hypersurfaces are given.
Keywords: Helicoidal hypersurfaces of Dini-type, Gaussian curvature, mean curvature, Minkowski
4-space.
References:
[1] K. Arslan, R. Deszcz, Ş. Yaprak, On Weyl pseudosymmetric hypersurfaces. Colloq. Math. 72-
2, 353-361 (1997).
[2] B.Y. Chen, Total mean curvature and submanifolds of finite type. World Scientific, Singapore,
1984.
[3] U. Dini, Sopra le funzioni di una variabile complessa, Annali di matematica pura ed applicate.
4(2), 159-174; in [Dini, Opere, II, 245-263] (1871).
[4] E. Güler, A. Gümüşok Karaalp, M. Magid, Dini-type helicoidal hypersurface in 4-space
(submitted).
[5] E. Güler, H.H. Hacısalihoğlu, Y.H. Kim, The Gauss map and the third Laplace-Beltrami operator
of the rotational hypersurface in 4-space (submitted).
[6] E. Güler, G. Kaimakamis, M. Magid, Helicoidal hypersurfaces in Minkowski 4-space E₁⁴
(submitted).
[7] E. Güler, M. Magid, Y. Yaylı, Laplace Beltrami operator of a helicoidal hypersurface in four
space. J. Geom. Sym. Phys. 41, 77-95 (2016).
[8] E. Güler, N.C. Turgay, Cheng-Yau operator and Gauss map of rotational hypersurfaces in 4-
space (submitted).
[9] M. Magid, C. Scharlach, L. Vrancken, Affine umbilical surfaces in R⁴. Manuscripta Math. 88,
275-289 (1995).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
36
TORUS HYPERSURFACE IN 4-SPACE
Erhan GÜLER1, Ömer KiŞi2
1,2Bartın University, Faculty of Science, Department of Mathematics, 74100 Bartın, Turkey
eguler@bartin.edu.tr
okisi@bartin.edu.tr
Abstract: Torus hypersurface is defined in the four dimensional Euclidean space. Equations for the
Gaussian and mean curvature are derived and some examples of the projection surfaces are given.
Keywords: Torus hypersurface, Gaussian curvature, mean curvature, Euclidean 4-space.
References:
[1] Abbena,E. Salamon S., Gray A. Modern Differential Geometry of Curves and Surfaces with
Mathematica, Chapman and Hall/CRC, 2006.
[2] Banchoff T.F., Lovett S.T. Differential Geometry of Curves and Surfaces. A K Peters/CRC
Press, 2010.
[3] Chen B.Y. Total mean curvature and submanifolds of finite type. World Scientific, Singapore,
1984.
[4] Cheng, Q.M. Wan, Q.R. Complete hypersurfaces of R⁴ with constant mean curvature. Monatsh.
Math. 118 3-4, 171-204 (1994).
[5] Cheng S.Y., Yau S.T. Hypersurfaces with constant scalar curvature. Math. Ann., 225 195—204
(1977).
[6] Dillen F., Pas J., Verstraelen L. On surfaces of finite type in Euclidean 3-space. Kodai Math. J.
13, 10-21 (1990).
[7] Do Carmo M., Dajczer M. Rotation Hypersurfaces in Spaces of Constant Curvature. Trans.
Amer. Math. Soc. 277, 685-709 (1983).
[8] Ferrandez A., Garay O.J., Lucas P. On a certain class of conformally at Euclidean
hypersurfaces. Proc. of the Conf. in Global Analysis and Global Differential Geometry, Berlin, 1990.
[9] Ganchev G., Milousheva V. General rotational surfaces in the 4-dimensional Minkowski space.
Turkish J. Math. 38, 883-895 (2014).
[10] Magid M., Scharlach C., Vrancken L. Affine umbilical surfaces in R⁴. Manuscripta Math. 88
(1995) 275-289.
[11] Moore C. Surfaces of rotation in a space of four dimensions. Ann. Math. 21 (1919) 81-93.
[12] Moore C. Rotation surfaces of constant curvature in space of four dimensions. Bull. Amer. Math.
Soc. 26 (1920) 454-460.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
37
ON QUASI-LACUNARY INVARIANT CONVERGENCE OF SEQUENCES OF
SETS
Esra GÜLLE, Uğur ULUSU
Department of Mathematics, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey,
egulle@aku.edu.tr ulusu@aku.edu.tr
Abstract: In this study, we give definitions of Wijsman quasi-lacunary invariant convergence,
Wijsman strongly quasi-lacunary invariant convergence and Wijsman quasi-lacunary invariant
statistically convergence for sequences of sets. We also examine the existence of some relations
among these definitions and some convergences types for sequences of sets given in [4, 5], too.
Keywords: statistical convergence, invariant convergence, quasi-invariant convergence, lacunary
sequence, sequences of sets, Wijsman convergence.
References:
[1] G.Beer, Wijsman convergence: A survey, Set-Valued Analysis, 2 (1994), 77-94.
[2] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
[3] J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific Journal of Math. 160(1)
(1993), 43-51.
[4] E. Gülle and U. Ulusu, Wijsman quasi-invariant convergence, Filomat, (submitted for publication).
[5] N. Pancaroğlu and F. Nuray, Lacunary invariant statistical convergence of sequences of sets with
respect to a modulus function, Journal of Mathematics and System Science, 5 (2015), 122-126.
[6] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30(1)
(1963), 81-94.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
38
SOME FIXED POINT RESULTS FOR A NEW THREE STEPS ITERATION
PROCESS IN BANACH SPACES: A REVISIT
Faik GÜRSOY1, Müzeyyen ERTÜRK2, Vatan KARAKAYA3
1,2Department of Mathematics, Adiyaman University,02040 Adiyaman, Turkey,
faikgursoy02@hotmail.com
merturk3263@gmail.com
2 Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210
Istanbul,Turkey,
vkkaya@yahoo.com
Abstract: In this presentation, a recently published paper by Karakaya et al. [Some fixed point results
for a new three steps iteration process in Banach spaces, Fixed Point Theory, 18 (2017), No. 2, 625-
640] revisited. The obtained results in this revisit are substantially improve the results reported in the
mentioned paper.
Keywords: Almost contraction mappings, three-step iterative algorithm, strong convergence, data
dependency.
References:
[1] Karakaya, V, Atalan, Y, Doğan, K, El Houda Bouzara, N, Some fixed point results for a new
three steps iteration process in Banach spaces, Fixed Point Theory 18, 625-640 (2017)
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
39
AN APPLICATION OF THREE DIMENSIONAL CELLULAR AUTOMATA
WITH PBC
Ferhat SAH
Department of Mathematics, Adiyaman University, Adiyaman, Turkey,
fsah@adiyaman.edu.tr
Abstract: In this study we give an application of CA based bit error correcting codes by applying
reversible CA which fall into a 3D-CA family with periodic boundary condition. we also compare the
classical syndrome decoding with the one introduced
Keywords: error correcting codes, periodic boundary condition, characteristic matrix
References:
[1] D.R. Chowdhury, S. Basu, I.S. Gupta and P.P. Chaudhuri, Design of CAECC- Cellular Automata
Based Error Correcting Code,IEEE Trans. Computers, 43 (1994) 759-764.
[2] M.E.Koroglu, I.Siap and H. Akın, Error correcting codes via reversible cellular automata over
finite fields, The Arabian Journal for Science and Engineering, vol.39, pp.1881-1887, (2014)
[3] Siap, I., Akin, H., and Koroglu, M. E. Reversible cellular automata with penta- cyclic rule and
ECCs. International Journal of Modern Physics C, 23(10), 1250066, (2012).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
40
AN APPLICATION OF ONE DIMENSIONAL CELLULAR AUTOMATA UNDER
INTERMEDIATE BOUNDARY CONDITION
Ferhat SAH
Department of Mathematics, Adiyaman University, Adiyaman, Turkey,
fsah@adiyaman.edu.tr
Abstract: In this study we give some important definitions and then we talk about some dvantages
error correcting codes and its applications.Finally, we present an application of CA based bit error
correcting codes by applying reversible CA which fall into a CA family with inter-mediate boundary
condition.
Keywords: error correcting codes, periodic boundary condition,
characteristic matrix
References:
[1] D.R. Chowdhury, S. Basu, I.S. Gupta and P.P. Chaudhuri, Design of CAECC-Cellular Automata
Based Error Correcting Code, IEEE Trans. Computers, 43 (1994) 759-764.
[2] M.E.Koroglu, I.Siap and H. Akın, Error correcting codes via reversible cellular automata over
finite fields, The Arabian Journal for Science and Engineering, vol.39,pp.1881-1887, (2014)
[3] Siap, I., Akin, H., and Koroglu, M. E. Reversible cellular automata with penta- cyclic rule and
ECCs. International Journal of Modern Physics C, 23(10), 1250066, (2012).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
41
NUMERICAL APPROACH BASED ON LAGRANGE POLYNOMIALS FOR
SOLVING FREDHOLM INTEGRAL EQUATIONS
Fernane KHAIREDDINE
Department of Mathematics, Laboratory of Applied Mathematics and Modeling,University of 8 May 1945
Guelma, Algeria
kfernane@yahoo.fr
Abstract: In this paper, we introduce a numerical method for solving linear Fredholm integral
equations of the second type. To solve these equations, we consider the equation solution
approximately from Lagrange Polynomials Method. The numerical solution of a linear integral
equations equation is reduced to solving a linear system of algebraic equations. Also, some
numerical examples is presented to show the efficiency of the method.
Keywords: Fredholm integral equations, Lagrange Polynomials, Taylor polynomials. Operational
matrix
References:
[1] L. Bougoffa, R. C. Rach and A. Mennouni, An approximate method for solving a class of weakly-
singular Volterra integro-differential equations. Appl. Math. Comput. 217 (2011), no. 22, 8907--8913.
[2] H. Brunner, On the numerical solution of nonlinear Volterra-Fredholm integral equations by
collocation methods. SIAM J. Numer. Anal. 27 (1990), no. 4, 987--1000.
[3] A. Chakrabarti and A. J. George, A formula for the solution of general Abel integral equation.
Appl. Math. Lett. 7 (1994), no. 2, 87--90.
[4] A. Zerarka *, A. Soukeur, A generalized integral quadratic method: I. an efficient solution for
one-dimensional Volterra integral equation, Communications in Nonlinear Science and Numerical
Simulation 10 (2005) 653–663.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
42
SOME BOUNDS OF THE FINITE HILBERT TRANSFORM AND
APPLICATIONS IN NUMERICAL INTEGRATION
Fuat USTA
Department of Mathematics, Düzce University, Konuralp Campus, 81620, Düzce, Turkey,
fuatusta@duzce.edu.tr
Abstract: The finite Hilbert transform is a useful tool in fields like time series analysis, signal
processing, radar systems, aerodynamics, the theory of elasticity, and other areas of the engineering
sciences. In this study, some explicit bounds and approximations for the finite Hilbert transform are
given for absolutely continuous mappings. Then, some numerical experiments for the obtained
approximation are also presented.
Keywords: Finite Hilbert Transform, Cauchy Principal Value, Numerical Integration.
References:
[1] N. M. Dragomir, S. S. Dragomir, P. M. Farrell and G. W. Baxter, A quadrature rule for the finite
Hilbert transform via trapezoid type inequalities, J. Appl. Math. Comput. 13 (2003), no. 1-2, 6784.
[2] N. M. Dragomir, S.S. Dragomir & P. Farrell, Approximating the finite Hilbert transform via
trapezoid type inequalities, Comput. Math. Appl. 43 (2002), 10-11, 13591369.
[3] W. J. Liu and N. Lu, Approximating the finite Hilbert Transform via Simpson type inequalities
and applications, Politehnica University of Bucharest Scientic Bulletin-Series A-Applied Mathematics
and Physics, 77 (2015), no. 3, 107-122.
[4] W. Liu, X. Gao and Y. Wen, Approximating the finite Hilbert transform via some companions of
Ostrowski’s inequalities. Bull. Malays. Math. Sci. Soc. 39 (2016), no. 4, 1499-1513.
[5] N. Ujevic, A generalization of Ostrowskis inequality and applications in numerical integration,
Appl. Math. Lett., 17 (2004), 133137.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
43
P-3-PRIME IDEALS IN NEAR RINGS
Funda TAŞDEMİR1, İsmail TAŞTEKİN2
1Department of Mathematics, Yozgat Bozok University, 66100 Yozgat, Turkey,
funda.tasdemir@bozok.edu.tr
2Sorgun Türk Telekom Anatolian High School, 66700 Yozgat, Turkey,
ismail.tastekin.s@gmail.com
Abstract: In this talk, we introduce the notion of P-3-prime ideals, where P is an ideal of a near-ring.
Then, we obtain some relationships between P-3-prime ideal and P-c-prime ideal. It is proved that a
P-c-prime ideal is also a P-3-prime ideal. But the converse holds under some conditions. We provide
examples to illustrate our results.
Keywords: near ring, P-3-prime ideal, P-c-prime ideal.
References:
[1] Pilz, G., Near-rings, 2nd Ed., Amsterdam, New York, Oxford, North-Holland, 1983.
[2] Dheena, P. and Jenila, C., P-Strongly Regular Near-rings, Journal of the Korean Mathematical
Society, 27, 501-506, 2012.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
44
ON INCLUSION THEOREMS FOR ABSOLUTE CESÀRO SUMMABILITY
METHODS
G. Canan HAZAR GÜLEÇ1, M. Ali SARIGÖL2
1,2Department of Mathematics, Pamukkale University, Kınıklı Campus, 20070 Denizli, Turkey,
gchazar@pau.edu.tr
msarigol@pau.edu.tr
Abstract: In this study, we give necessary and sufficient condition in order that |𝐶, −1|𝑘 ⇒ |𝐶, 𝛼| for
the case 𝛼 > −1 and 𝑘 > 1, so we also complete some open problems in this concept.
Keywords: Sequence spaces, Absolute Cesàro summability, Inclusion relations.
References:
[1] Flett, T.M: On an extension of absolute summability and some theorems of Littlewood and
Paley, Proc. London Math. Soc. 7, 113-141 (1957).
[2] Hardy, G. H: Divergent Series, Oxford, 1949.
[3] Hazar, G. C, Sarıgöl M. A: Compact and Matrix Operators on the Space |𝐶, −1|𝑘, J. Comput.
Anal. Appl., 25(6), 1014-1024 (2018).
[4] Sarıgöl, M.A: Extension of Mazhar's theorem on summability factors, Kuwait J. Sci. 42 (3), 28-
35 (2015).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
45
ON THE ZERO POINT PROBLEM OF MONOTONE OPERATORS IN CAT(0)
SPACES
G. Zamani ESKANDANI1, M. RAEISI 2
1,2Department of Pure Mathematics, Faculty of Mathematical Sciences University of Tabriz, Tabriz, Iran,
zamani@tabrizu.ac.ir
m.raeisi@tabrizu.ac.ir
Abstract: In this paper, a common zero of a finite family of monotone operators and a common
fixed point of an infinitely countable family of quasi-nonexpansive mappings are approximated in
reflexive CAT(0) spaces. In addition, we define a norm on span X* and give an application of this
norm, where X is a CAT(0) space with dual space.
Keywords: Proximal point algorithm, CAT(0) spaces , monotone operator
References:
[1] Espinola, R, Fernandez-Leon, A: CAT(κ)-Spaces, weak convergence and fixed points. J. Math.
Anal. Appl. 353, 410-427 (2009)
[2] M. Bridson and A. Haefliger, Metric Spaces of Non-positive Curvature, Springer-Verlag, Berlin,
Heidelberg, 1999
[3] Kakavandi, B.A., Amini, M.: Duality and subdifferential for convex functions on
complete C A T(0) metric spaces. Nonlinear Anal. 73, 3450–3455 (2010)
[4] Khatibzadeh, H., Ranjbar, S.: Monotone operators and the proximal point algorithm in
complete C A T(0) metric spaces. J. Aust. Math. Soc. 103, 70–90 (2017)
[5] G.Z. Eskandani and M. Raeisi, On the zero point problem of monotone operators in
Hadamard spaces. Numer Algor (2018). https://doi.org/10.1007/s11075-018-0521-3
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
46
ON MIZOGUCHI-TAKAHASHI'S TYPE SET VALUED
(α-θ) CONTRACTIONS
Gonca DURMAZ1, İshak ALTUN2, Murat OLGUN3 ,Hatice ASLAN HANÇER4
1 Department of Mathematics, Faculty of Science, Çankırı Karatekin Universty, 18100, Çankırı, Turkey,
gncmatematik@hotmail.com
2,4 Department of Mathematics, Faculty of Science and Art, Kirikkale Universty, Yahşihan, Kirikkale, Turkey
ishakaltun@yahoo.com , haslan@kku.edu.tr
3 Department of Mathematics, Faculty of Science, Ankara Universty, 06100, Tandoğan, Ankara
olgun@ankara.edu.tr
Abstract: The aim of this talk is to present a new approach to fixed point theorems for multivalued
mappings on complete metric spaces. To do this, we introduce a new concept called MT-type (α-θ)-
contraction and prove fixed point result for such mappings. Also, we present some examples showing
that our result is a real generalization of some existing results.
Keywords: Fixed point, MT-type, complete metric space.
References:
[1] I. Altun, H. A. Hançer and G. Mınak, On a board category of multivalued weakly Picard
operators, Fixed Point Theory, 18(1), 2017, 229-236.
[2] G. Durmaz, Some theorems for a new type of multivalued contractive maps on metric space,
Turkish Journal of Mathematics, 41(4), 2017, 1092-1100.
[3] M. Jleli and B. Samet, A new generalization of the Banach contraction principle, J. Ineq. Appl.,
2014, 2014:38 8 pp.
[4] N. Mizoguchi and W. Takahashi, Fixed point theorems for multivalued mappings on complete
metric space, Journal of Mathematical Analysis and Applications, 141(1998), 177-188.
[5] B. Samet, C. Vetro, and P. Vetro, Fixed point theorems forα-ψ contractive type mappings,
Nonlinear Analysis. Theory, Methods and Applications, 75(4), 2012, 2154–2165.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
47
NOVEL CONTOUR SURFACES TO THE (2+1)-DIMENSIONAL DATE–JIMBO–
KASHIWARA–MIWA EQUATION
Haci Mehmet BASKONUS
Department of Computer Engineering, Munzur University, Tunceli, Turkey
hmbaskonus@gmail.com
Abstract: In this manuscript, improved Bernoulli sub-equation function method based on the
Bernoulli differential method is considered. This method is based on the converting the (2+1)-
dimensional Date–Jimbo–Kashiwara–Miwa equation into ordinary differential equation. Some new
solutions such as complex and exponential are obtained. To better understanding of physical
meanings of model are introduced by plotting two- and three-dimensional surfaces along with contour
simulations. Finally, a conclusion is presented by mentioning important acquisitions founded in this
study.
Keywords: Improved Bernoulli sub-equation function method; (2+1)-dimensional Date–Jimbo–
Kashiwara–Miwa Equation; Complex Exponential function solution.
References:
[1] B. Zheng, “A New Bernoulli Sub-Ode Method For Constructing Traveling Wave Solutions For
Two Nonlinear Equations With Any Order”, U.P.B. Sci. Bull., Series A, 73.3, (2011): 1-10.
[2] X.F. Yang, Z.C. Deng and Y. Wei, “A Riccati-Bernoulli sub-ODE method for nonlinear partial
differential equations and its application”, Advances in Difference Equations, 117, (2015): 1-17.
[3] Y.Q.Yuan, B.Tian, W.R. Sun, J.Chai, L.Liu, “Wronskian and Grammian solutions for a (2+1)-
dimensional Date–Jimbo–Kashiwara–Miwa equation”, Computers & Mathematics with
Applications,74.4,(2017): 873-879.
[4] J.C. Pu, H.C. Hu, “Exact solitary wave solutions for two nonlinear systems, Indian Journal of
Physics”, https://doi.org/10.1007/s12648-018-1267-4
[5] B. Zheng, “Application of A Generalized Bernoulli Sub-ODE Method For Finding Traveling
Solutions of Some Nonlinear Equations”, WSEAS Transactions on Mathematics, 7.11, (2012): 618-
626.
[6] H.M.Baskonus, H.Bulut and D.G.Emir, “Regarding New Complex Analytical Solutions for the
Nonlinear Partial Vakhnenko-Parkes Differential Equation via Bernoulli Sub-Equation Function
Method”, Mathematics Letters, 1.1, (2015): 1-9.
[7] H.M.Baskonus, H.Bulut, “On the Complex Structures of Kundu-Eckhaus Equation via Improved
Bernoulli Sub-Equation Function Method”, Waves in Random and Complex Media, 25.4, (2015): 720-
728.
[8] H.M.Baskonus, H.Bulut, “An Effective Scheme for Solving Some Nonlinear Partial Differential
Equation Arising In Nonlinear Physics”, Open Physics, 13.1, (2015): 280–289.
[9] H.M.Baskonus and H.Bulut, “Exponential Prototype Structures for (2+1)-Dimensional Boiti-
Leon-Pempinelli Systems in Mathematical Physics”, Waves in Random and Complex Media, 26.2,
(2016): 201-208.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
48
ON THE ROOTS OF AN EVOLUTION EQUATION
Haci Mehmet BASKONUS
Department of Computer Engineering, Munzur University, Tunceli, Turkey
hmbaskonus@gmail.com
Abstract: In this paper, we apply Bernoulli sub-equation function method to the model which reads
as ‘S-Integrable’ evolution equation. Complex and exponential functional roots are obtained. Plotting
two- and three-dimensional surfaces along with contour simulations give rise to more sophisticated
information about the model. At the end of the paper, we present a conclusion by giving vital
informations about the surfaces of roots.
Keywords: Bernoulli sub-equation function method; ‘S-Integrable’ evolution equation; Complex,
Exponential roots.
References:
[1] Kundu A. Landau–Lifshitz and higher-order nonlinear systems gauge generated from nonlinear
Schrödinger-type equations. J. Math. Phys. 25, (1984), 3433–3438.
[2] Guangxue Zhang , Lili Zhang , Jinqing Wang , Zuohe Chi , A new model for the acoustic wake
effect in aerosol acoustic agglomeration processes, Applied Mathematical Modelling (2018), doi:
10.1016/j.apm.2018.03.027
[3] Ruiqing Ming, Huiqun He, Qiangfa Hu, A new model for improving the prediction of liquid loading
in horizontal gas wells, Journal of Natural Gas Science & Engineering (2018), doi: 10.1016/
j.jngse.2018.06.003.
[4] Jun Bi, Mingyi Zhang, Wenwu Chen, Jianguo Lu, Yuanming Lai, A new model to determine the
thermal conductivity of fine-grained soils, International Journal of Heat and Mass Transfer 123,
(2018) 407–417.
[5] Chunga K, Toulkeridis T. First evidence of aleo-tsunami deposits of a major historic event in
Ecuador. J. Tsunami Soc. Int. 33, (2014);33:55–69.
[6] X.F. Yang, Z.C. Deng and Y. Wei, “A Riccati-Bernoulli sub-ODE method for nonlinear partial
differential equations and its application”, Advances in Difference Equations, 117, (2015): 1-17.
[7] Y.Q.Yuan, B.Tian, W.R. Sun, J.Chai, L.Liu, “Wronskian and Grammian solutions for a (2+1)-
dimensional Date–Jimbo–Kashiwara–Miwa equation”, Computers & Mathematics with
Applications,74.4,(2017): 873-879.
[8] J.C. Pu, H.C. Hu, “Exact solitary wave solutions for two nonlinear systems, Indian Journal of
Physics”, https://doi.org/10.1007/s12648-018-1267-4
[9] E.Yüce, A.Ö. Tarakçıoğlu, Attitudes of Computer Engineering Department Students towards
ESP Courses Integrated to Foreign Language Courses: Tunceli University Case, Bilim ve Gençlik
Dergisi, 1.1: (2013), 1-12.
[10] E.Yüce, “An investigation into the Relationship between EFL Learners’ Foreign Music Listening
Habits and Foreign Language Classroom Anxiety”, International Journal of Languages’ Education
and Teaching, 6(2), (2018): 471-482.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
49
SOME CARISTI TYPE FIXED POINT THEOREMS ON M-METRIC SPACE
Hakan SAHIN1,3, İshak ALTUN2, Duran TURKOGLU3, Hatice ASLAN HANCER2
1Department of Mathematics, Amasya University, Faculty of Science, Amasya, Turkey
hakan.sahin@amasya.edu.tr
2Department of Mathematics, Kırıkkale University, Faculty of Science, Kırıkkale, Turkey,
ishakaltun@yahoo.com, haslan@kku.edu.tr
3Department of Mathematics, Gazi University, Faculty of Science, Ankara, Turkey,
dturkoglu@gazi.edu.tr
Abstract: Recently, concept of M-metric which is extension of partial metric and usual metric is
defined by Asadi et al. In this paper, we prove caristi type fixed point theorem and then, we give
some generalizations of caristi type fixed point theorem on M-metric space. Finally, we support our
idea with nontrivial examples.
Keywords: fixed point, caristi type, M-metric
References:
[1] Asadi, M, Karapınar, E, and Salimi, P: New extension of p-metric spaces with some fixed point
results on M-metric spaces. Journal of Inequalities and Applications, 2014 (2014): 18
[2] Caristi, J: Fixed point theorems for mapping satisfying inwardness conditions. Trans. Amer.
Math. Soc. 215, 241-251 (1976)
[3] Bae, J. S: Fixed point theorems for weakly contractive multvalued maps. J. Math. Anal. App. 28,
690-697 (2003)
[4] Suzuki, T: Generalized Caristi’s fixed point theorems by Bae and others. J. Math. Anal. App.
302, 502-508 (2005)
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
50
QUASI-HAUSDORFF TRANSFORMATIONS FOR DOUBLE SEQUENCES
Hamdullah ŞEVLİ
İstanbul Ticaret University
Abstract: Quasi-Hausdorff transformations for single sequences were defined by Hardy [1]. The aim
of this presentation is to extend to double sequences some of the results which have been proved
for Quasi-Hausdorff matrices.
Keywords: Quasi-Hausdorff matrices, double series, absolute summability.
AMS 2010. 40F05, 40G05.
References:
[1] Hardy, G.H., Divergent series, Clarendon Press, Oxford, 1949.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
51
WEIGHTED COMPOSITION OPERATORS FROM BLOCH-TYPE SPACES
INTO BERS-TYPE SPACES
Hamid VAEZI1, Mohamad NAGHLISAR2
1,2Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran,
hvaezi@tabrizu.ac.ir
m.naghlisar@tabrizu.ac.ir
Abstract: In this paper we consider the weighted composition operator from Bloch-type space 𝐵𝛼
into Bers-type space 𝐻𝛽∞ in three cases, α >1 , α =1 and α <1. We give necessary and sufficient
conditions for boundedness and compactness of the above operator.
Keywords: Weighted composition operator, Bloch-type space, Bers-type
space, Boundedness, Compactness.
References:
[1] Colonna F. and Li S., Weighted composition operator from the Besov spaces to the Bloch
spaces, Bull. Malaysian Sci. Soc., 36(4) (2013),1027-1039.
[2] Cowen C. C. and Maccluer B. D., Composition operators on spaces of analytic functions,
Studies in Advanced Math., CRC Press, Boca Raton (1995).
[3] Hassanlou, M., Vaezi H. and Wang M., Weighted composition operators on weak vector-valued
Bergman spaces and Hardy spaces, Banach J. Math. Anal., 9(2) (2015), 35-43.
[4] Weixian H. and Lijian j., Composition operator on Bers-type spaces, Acta. Math. Sci., 22B(3)
(2002), 404-412.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
52
ON SEMICOMMUTATIVE RINGS
Handan KOSE
Kırşehir Ahi Evran University, Department of Mathematics, Kırşehir
handan.kose@ahievran.edu.tr
Abstract: A ring 𝑅 is called semicommutative if for any 𝑎, 𝑏 ∈ 𝑅, 𝑎𝑏 = 0 implies 𝑎𝑅𝑏 = 0. The ring 𝑅
is semicommutative if and only if any right (left) annihilator over 𝑅 is an ideal of 𝑅 by [1, Lemma 1] or
[2, Lemma 1.2]. A ring 𝑅 is called nil-semicommutative [3] if 𝑎𝑏 = 0 implies 𝑎𝑅𝑏 = 0 for every nilpotent
elements 𝑎, 𝑏 ∈ 𝑅. Another version of semicommutativity is weak semicommutativity. The ring 𝑅 is
called weakly semicommutative if for any 𝑎, 𝑏 ∈ 𝑅, 𝑎𝑏 = 0 implies 𝑎𝑟𝑏 is nilpotent for any 𝑟 ∈ 𝑅.
In this work, we study some cases when an amalgamated construction 𝐴 ⋈𝑓 𝐼 ≔ {(𝑎, 𝑓(𝑎) + 𝑖): 𝑎 ∈
𝐴, 𝑖 ∈ 𝐼} of a ring 𝐴 along an ideal 𝐼 of a ring 𝐵 with respect to a ring homomorphism 𝑓 from 𝐴 to 𝐵,
is semicommutative, nil-semicommutative and weakly semicommutative.
Keywords: Semicommutative ring, nil-semicommutative ring and weakly semicommutative ring.
Acknowledgement: This work was supported by the Ahi Evran University Scientific Research
Projects Coordination Unit. Project Number: FEF. A4. 18. 008
References:
[1] C. Huh, Y. Lee, A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra,
2002, 30(2), 751-761.
[2] G. Shin, Prime ideals and sheaf representations of a pseudo symmetric ring, Trans. Amer. Math.
Soc., 1973, 184, 43-60.
[3] R. Mohammadi, A. Moussavi, M. Zahiri, On nil-semicommutative rings, Int. Electron. J. Algebra,
2012, 11, 20-37.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
53
SOME OPERATOR INEQUALITIES
Havva TİLKİ1, Mualla Birgül HUBAN2, Mehmet GÜRDAL3
1Department of Mathematics, Süleyman Demirel University, East Campus, 32100 Isparta, Turkey,
havvatilki32@gmail.com
2 Department of Mathematical Engineering, Süleyman Demirel University, East Campus, 32100 Isparta,
Turkey,
btarhan03@yahoo.com
3 Department of Mathematical Engineering, Süleyman Demirel University, East Campus, 32100 Isparta,
Turkey,
gurdalmehmet@sdu.edu.tr
Abstract: In this paper, we will use some known operator inequalities for proving some new
inequalities for the Berezin number of operators acting on the reproducing kernel Hilbert spaces.
Keywords: Reproducing kernel Hilbert space, Berezin symbol, Berezin number, quasi-paranormal
operator, Hölder-McCarthy type inequality, Young type inequality.
References:
[1] Aronszajn, N., Theory of Reproducing Kernel. Trans American Mathematical Society, 68 (1950),
337-404.
[2] Karaev, M.T., Gürdal, M., Huban, M.B., Reproducing kernels, Engliš algebras and some
applications. Studia Mathematica, 232(2) (2016), 113-141.
[3] Karaev, M.T., Gürdal, Okudan, A., Hardy-Hilbert inequality and Power inequalities for Berezin
numbers of operators, Math. Inequal. Appl., 19(3), (2016) 883-891.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
54
EPI EULER CONVERGENCE OF KIND CONVERGENT SETS
Harun POLAT
Muş Alparslan University Art and Science Faculty, Department of Mathematics, 49100 Muş,Turkey.
h.polat@alparslan.edu.tr
Abstract: There are different convergence notions for sequence of sets, which have significance for
certain applications. Kuratowski convergence, Hausdorff convergence, Wijsman convergence,
Fisher convergence and Mosco convergence are the best known types of convergence. In this paper
we peresent definitions Epi EulerConvergence of Kuratowski convergence, Epi Euler Convergence
of Hausdorff convergence, Epi Euler Convergence of Wijsman convergence, Epi Euler Convergence
of Fisher convergence and Epi Euler Convergence of Mosco convergence of sequences of sets. Also
we characterize the connection between of their.
Keywords: Epi Euler convergence, Kuratowski, Hausdorff, Wijsman, Fisher and Mosco
convergence.
References:
[1] C. Kuratowski, Topology, Academic Press, New York, 1966.
[2] F. Hausdorff , Grundzuge derMengenlehre, Verlag von Veit, Leipzig, Reprinted by Chelsea, New
York1914.
[3] R. A. Wijsman,” Convergence of sequences of convex sets, cones and functions”, Bull. Amer.
Math. Soc. 70 (1964) 186-188.
[4] B. Fisher, “Common fixed points of mappings and set-valued mappings”, Rostock Math. Kolloq.
18 (1981) 69-77.
[5] U. Mosco, “Convergence of convex sets and of solutions of variational inequalities”, Adv. in Math.
3 (1969), 510--585.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
55
NEW TOPOLOGY IN 𝜷(𝑰)
Hassan MOUADI1, Driss KARIM2
1Faculty of Sciences and Techniques , University HASSAN 2, Mohammedia, Morocco.
hassanmouadi@hotmail.com
2 Department of Mathematics, Faculty of Sciences and Techniques , University HASSAN 2, Mohammedia,
Morocco.
dkarim@ced.uca.ma
Abstract: In this study, we give definition of F-topology in β(I) set of all ultrafilter in I and give some
propriety of maximal and prime ideals of product of infinity rings (I is the index set)
Keywords: ultrafilter , nilpotent index, F-lim, F-topology.
References:
[1] M.F. Atiyah and I.G. Macdonald, Introduction to commutative algebra, Addison-Wesley, 1969
[2] M. Fontana and K. A. Loper, The patch topology and the ultrafilter topology on the prime
spectrum of a commutative ring, Comm. Algebra 36(2008), 2917-2922
[3] Jay. Shapiro, The Prime Spectrum of an Infinite Product of Zero-Dimensional Rings, Zero-
Dimensional Commutative Rings, 1995
[4] S. Garcia-Ferreira and L. M. Ruza-Montilla, The F-lim of a Sequence of Prime Ideals,
Communications in Algebra 39(7):2532-2544 _ July 2011
[5] L.Gillman and M. Heinzer, Product of commutative rings and zero dimensionality,Trans. Amer.
Math. Soc.,331 (1992), 663-680.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
56
INVESTIGATION OF SUBORBİTAL GRAPHS OF THE
TYPE
𝜞𝟎(𝑳, 𝑴) = (𝒂 𝒃𝑴
𝒄𝑳 𝒅)
İbrahim GÖKCAN
Department of Mathematics, Institute of Science and Technology,Karadeniz Technical University, Trabzon,
Turkey,
gokcan4385@gmail.com
Abstract: In this study, the definition of suborbital graphs of the type 𝛤0(𝐿, 𝑀) = (𝑎 𝑏𝑀𝑐𝐿 𝑑
), its
transitive and invariant state on the set of generalized rational numbers, basic congruence groups,
number of basic congruence groups and some of its other features have been tried to be examined
with the help of definitions and theories of basic graph theories. 𝛤0(n) ≔ {(𝑎 𝑏𝑐 𝑑
) ∈ Γ|𝑐 ≡
0 mod n } is connected to the congruential basis 𝑛 and 𝛤0(𝐿, 𝑀) = {( 𝑎 𝑏𝑀𝑐𝐿 𝑑
) ∈ 𝛤|𝑎, 𝑏, 𝑐, 𝑑 ∈
ℤ ve 𝑎𝑑 − 𝑏𝑐(𝐿𝑀) = 1 } is connected to 𝐿. Furthermore, it has been shown that 𝛤0(𝐿, 𝑀) moves
on ℚ̂ in an imprimitive way, thus, by defining the G-invariant equivalence relation, a different equation
relation on 𝛤0(𝐿, 𝑀) is defined which is different from universal and identity equivalence relations.
Keywords: Suborbital Graphs, Basic Congruence Groups, Transitive and Invariant.
References:
[1] Akbaş, M., On Suborbital Graphs for Modular Group, Bull. London Math. Soc., 33 (2011), 647-
652.
[2] Jones, G.A., Singerman, D. Ve Wicks, K., The Modular Group and Generalized Farey Graphs,
London Math. Soc. Lecture Notes, CUP, Cambridge, 160 (1991) 316-338.
[3] Ünal, H., Alt Yörüngesel Graflar ve Fibonacci Sayıları, Yüksek Lisans Tezi, K.T.Ü, Fen Bilimleri
Enstitüsü, Trabzon, 2013.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
57
WEIGHTED STOCHASTIC FIELD EXPONENT LEBESGUE AND SOBOLEV
SPACES
Ismail AYDIN1, Cihan UNAL2
1,2Department of Mathematics, Sinop University, Sinop, Turkey,
iaydin@sinop.edu.tr
cihanunal88@gmail.com
Abstract: In this study, we introduce weighted stochastic field exponent Lebesgue and Sobolev
spaces. After discussing some basic properties and embeddings of these spaces, we will want to
show an application of these spaces to the stochastic partial differential equations with stochastic
field growth.
Keywords: Weighted stochastic field exponent Lebesgue and Sobolev spaces, compact
embedding, weak solution, stochastic partial differential equation.
References:
[1] I. Aydın, Weighted Variable Sobolev Spaces and Capacity, Journal of Function Spaces and
Applications, Vol. 2012, Article ID 132690, (2012): 17 pages, doi:10.1155/2012/132690.
[2] B. Lahmi, E. Azroul and K. El Haiti, Nonlinear Degenerated Elliptic Problems with Dual Data and
Nonstandard Growth, Math. Reports, 20 (70). 1 (2018): 81-91.
[3] B. Tian, B. Xu and Y. Fu, Stochastic Field Exponent Function Spaces with Applications,
Complex Variables and Elliptic Equations, 59. 1 (2014): 133-148.
[4] C. Unal and I. Aydın, Weighted Variable Exponent Sobolev Spaces with Zero Boundary Values
and Capacity Estimates, Sigma J Eng & Nat Sci 36 (2), (2018): 371-386.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
58
SOME COMPACTNESS CRITERIONS IN WEIGHTED VARIABLE EXPONENT
AMALGAM SPACES
Ismail AYDIN1, Cihan UNAL2
1,2Faculty of Arts and Sciences, Department of Mathematics, Sinop University,
57000 Sinop, Turkey,
iaydin@sinop.edu.tr
cihanunal88@gmail.com
Abstract: In this study, we consider totally bounded subsets in weighted variable exponent amalgam
and Sobolev spaces. Moreover, we present some new conditions and criterions for compactness of
bounded subsets in these spaces.
Keywords: Weighted amalgam and Sobolev spaces, compactness, totally bounded sets
References:
[1] I. Aydın, On vector-valued classical and variable exponent amalgam spaces, Commun. Fac.
Sci. Univ. Ank. Series A1, 66(2), 100-114 (2017)
[2] R. Bandaliyev, Compactness criteria in weighted variable Lebesgue spaces, Miskolc Math.
Notes, 18(1), 95-101 (2017)
[3] P. Gorka, A. Macios, Almost everything you need to know about relatively compact sets in
variable Lebesgue spaces, J. Funct. Anal., 269(7), 1925-1949 (2015)
[4] H. Hanche-Olsen, H. Holden, The Kolmogorov-Riesz compactness theorem, Expo. Math.,
28(4), 385-394 (2010)
[5] A. N. Kolmogorov, Über Kompaktheit der Funktionenmengen bei der Konvergenz im Mittel,
Nachr. Ges. Wiss. Göttingen, 9, 60-63 (1931).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
59
CONVERGENCE ANALYSIS OF A NEW MODIFIED JUNGCK-THREE-STEP
ITERATIVE METHOD IN THE BANACH SPACES
Kadri DOĞAN1, Yılmaz ALTUN2
1Department of Computer Engineering , Artvin Coruh University, Artvin/Turkey
dogankadri@hotmail.com
2 Department of Mathematics, Ahi Evran University, Kırşehir, Turkey,
yılmazaltun@ahievran.edu.tr
Abstract: In this study, Some strong convergence results for modified Jungck-three-step iterative
scheme has been established in a Banach space. Comparison of this modified iteration scheme with
Jungck-three iterative scheme has been made by solving some scalar nonlinear equations.
Keywords: Jungck-type iterative process, Banach space, fixed point, strong convergence.
References:
[1] G. Jungck, Commuting Mappings and Fixed Points, Amer. Math. Monthly 83, No. 4 (1976) 261-
263.
[2] S. L. Singh, C. Bhatnagar and S. N. Mishra, Stability of Jungck-Type Iterative Procedures,
Internatioal J. Math. & Math. Sc. 19, (2005) 3035-3043.
[3] M. O. Olatiwo and C. O. Imor, Some Convergence results for the Jungck Mann and the Jungck
Ishikawa iteration process in the class of generalized zamfirescue operators,Acta Math. Univ.
Comenianae Vol. LXXVII, 2, (2008) 299-304.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
60
CONVERGENCE ANALYSIS OF JUNGCK-MP ITERATIVE METHOD IN THE
BANACH SPACES
Kadri DOĞAN1, Vatan KARAKAYA2
1Department of Computer Engineering , Artvin Coruh University, Artvin/Turkey
E-mail: dogankadri@hotmail.com
2 Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210
Istanbul,Turkey,
vkkaya@yahoo.com
Abstract: In this study, Some strong convergence results for modified Jungck-MP iteration schemes
have been established in a Banach space. Comparison of this modified iteration scheme with Jungck-
Ishikawa iteration scheme has been made by solving some scalar nonlinear equations.
Keywords: Jungck-MP iterative process, Banach space, fixed point, strong convergence. References: [1] G. Jungck, Commuting Mappings and Fixed Points, Amer. Math. Monthly 83, No. 4 (1976) 261-263 [2] S. L. Singh, C. Bhatnagar and S. N. Mishra, Stability of Jungck-Type Iterative Procedures, Internatioal J. Math. & Math. Sc. 19, (2005) 3035-3043.
[3] M. O. Olatiwo and C. O. Imor, Some Convergence results for the Jungck Mann and the Jungck Ishikawa iteration process in the class of generalized zamfirescue operators,Acta Math. Univ. Comenianae Vol. LXXVII, 2, (2008) 299-304.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
61
FIXED POINT THEOREMS VIA SIMULATION TYPE FUNCTIONS
Merve İLKHAN
Department of Mathematics, Düzce University, Düzce, Turkey,
merveilkhan@gmail.com
Abstract: The main goal of this study is to establish some results for the existence and uniqueness
of fixed points by the aid of simulation functions in the setting of generalized metric spaces.
Keywords: fixed point theorems, simulation functions, complete spaces.
References:
[1] S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations
integrals”, Fund. Math. 3 (1922) 133-181.
[2] F. Khojasteh, S. Shukla and S. Radenovic, “A new approach to the study of fixed point theorems via simulation functions”, Filomat 96 (2015) 1189-1194.
[3] A. Roldan-Lopez-de-Hierro, E. Karapinar , C. Roldan-Lopez-de-Hierro and J. Martinez
Morenoa, “Coincidence point theorems on metric spaces via simulation function”, J. Comput. Appl.
Math. 275 (2015) 345–355.
[4] C. Mongkolkeha, , Y. J. Cho and Poom Kumam, ” Fixed point theorems for simulation functions
in b-metric spaces via the wt-distance”, Appl. Gen. Topol. 18(1) (2017) 91-105.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
62
Δ - CONVERGENCE AND STRONG CONVERGENCE IN GENERALIZED CAT
(0) SPACES
Mohammad KNEFATI1 and Vatan KARAKAYA2
1Yildiz Technical University,Istanbul TURKEY
mknefati@gmail.com
2Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210
Istanbul,Turkey,
vkkaya@yahoo.com
Abstract: We establish strong and Δ - convergence for some iteration schames in generalized CAT
(0) spaces which is introduced by Khamsi [7].
References:
[1] M.A.Khamsi and S.Shukri,Generalized CAT(0) spaces.
[2] H.Fukharuddin and M.A.Khamsi,approximating common fıxed points in hyperbolic spaces.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
63
ON I2-CAUCHY DOUBLE SEQUENCES IN FUZZY NORMED SPACE
Muhammed Recai TÜRKMEN1, Erdinç DÜNDAR2
1Department of Mathematics, Faculty of Education, AfyonKocatepe University, 03200, Afyonkarahisar, Turkey,
mrtmath@gmail.com
2 Department of Mathematics, Faculty of Science and Literature, Afyon Kocatepe University, 03200,
Afyonkarahisar,Turkey,
edundar@aku.edu.tr
Abstract: In this study, we have investigated the concepts of I2-Cauchy and I2-convergence of
double sequences in fuzzy normed spaces. Also, we have investigated some properties and
relationships between these concepts.
Keywords: Double sequences, 2I convergence,
2I Cauchy,, Fuzzy normed spaces.
References:
[1] P. Das, P. Kostyrko, W. Wilczynski, P. Malik, I and I*-convergence of double sequences,
Math.Slovaca 58 (5) (2008), 605-620.
[2] E. Dündar, B. Altay, I2-convergence and I2-Cauchy of double sequences, Acta Mathematica
Scientia, 34(2) (2014), 343-353.
[3] E. Dündar, Ö. Talo, I2-convergence of double sequences of fuzzy numbers, Iranian Journal of
Fuzzy Systems Vol. 10, No. 3, (2013) pp. 37-50.
[4] E. Dündar, Ö. Talo, I2-Cauchy Double Sequences of Fuzzy Numbers, Gen. Math. Notes, 16(2)
(2013), 103-114.
[5] V. Kumar, On I and I*-convergence of double sequences, Math. Commun. 12 (2007), 171-181.
[6] V. Kumar, K. Kumar, On the ideal convergence of sequences of fuzzy numbers, Inform. Sci.,178
(2008), 4670-4678.
[7] M. R. Türkmen and M. Çınar, Lambda Statistical Convergence in Fuzzy Normed Linear Spaces,
Journal of Intelligent and Fuzzy Systems, 34 (6) (2018), 4023-4030
[8] L.A. Zadeh, Fuzzy sets, Information and Control 8(1965), 338-353.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
64
LACUNARY STATISTICAL CONVERGENCE IN FUZZY N-NORMED LINEAR
SPACES
Muhammed Recai TÜRKMEN
Department of Mathematics, Faculty of Education, AfyonKocatepe University, 03200 Afyonkarahisar, Turkey,
mrtmath@gmail.com
Abstract: In this paper, we introduced the concept of lacunary statistical summable and lacunary
statistical convergence in fuzzy n-normed linear spaces. It also has studied the some properties
these concepts.
Keywords: Lacunary convergence, Statistical convergence, Lacunary summable, Fuzzy n-normed
space.
References:
[1] H. Altınok, Y. Altın, and M. Et, Lacunary almost statistical convergence of fuzzy numbers, Thai
Journal of Mathematics, 2 (2) (2004), 265–274.
[2] J. A. Fridy and C. Orhan, Lacunary Statistical Convergence, Pasific Journal of Mathematics,
160 (1) (1993), 43–51.
[3] F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets
Systems, 99 (1998), 353–355.
[4] F. Nuray, U. Ulusu, and E. Dündar, Lacunary statistical convergence of double sequences of
sets, Soft Computing, 20 (7) (2016), 2883–2888.
[5] M. R. Türkmen and M. Çınar, Lacunary Statistical Convergence in Fuzzy Normed Linear
Spaces, Applied and Computational Mathematics, 6 (5) (2017), 233–237.
[6] M. R. Türkmen and H. Efe, On Some Properties Of Closability Of Farthest Point Maps in Fuzzy
n-Normed Spaces, imanager’s Journal on Mathematics, 2 (4) (2013), 33–38.
[7] M. R. Türkmen and E. Dündar, On lacunary statistical convergence of double sequences and
some properties in fuzzy normed spaces, Journal of Intelligent and Fuzzy Systems, DOI:10.
3233/JIFS-18841.
[8] L.A. Zadeh, Fuzzy sets, Information and Control 8(1965), 338-353.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
65
SOME RESULTS ON 𝝀 − STATISTICAL CONVERGENCE OF DOUBLE
SEQUENCES IN FUZZY NORMED SPACE
Muhammed Recai TÜRKMEN
Department of Mathematics, Faculty of Education, AfyonKocatepe University, 03200 Afyonkarahisar, Turkey,
mrtmath@gmail.com
Abstract: In this paper, we have introduced statistical convergence and condition of being
statistical Cauchy for double sequences in fuzzy normed linear spaces and we have studied some
results these concepts.
Keywords : Double sequences, Statistical convergence, statistical convergence, Fuzzy
normed space.
References:
[1] R. Çolak, On statistical convergence, Conference on Summability and Applications, May
12-13, (2011), Istanbul Turkey.
[2] M. Et ; M. Çınar and M. Karakaş, On statistical convergence of order of sequences of
function, J. Inequal. Appl., 204 (2013), 1-8.
[3] M. Mursaleen, statistical convergence, Math. Slovaca, 50(1) (2000), 111-115.
[4] E. Savas, On Strongly summable Sequences of Fuzzy Numbers, Information Science,
125(1-4) (2000), 181-186.
[5] F. Nuray, E. Savaş, Statistical convergence of sequences of fuzzy numbers, Math. Slovaca,
45(3) (1995), 269–273.
[6] M. R. Türkmen and M. Çınar, Lacunary Statistical Convergence in Fuzzy Normed Linear
Spaces, Applied and Computational Mathematics, 6 (5) (2017), 233–237.
[7] M. R. Türkmen and M. Çınar, Lambda Statistical Convergence in Fuzzy Normed Linear Spaces,
Journal of Intelligent and Fuzzy Systems, 34 (6) (2018), 4023-4030
[8] L.A. Zadeh, Fuzzy sets, Information and Control 8(1965), 338-353.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
66
LACUNARY I-CONVERGENCE IN FUZZY NORMED SPACES
Muhammed Recai TÜRKMEN
Department of Mathematics, Faculty of Education, Afyon Kocatepe University, 03200 Afyonkarahisar, Turkey,
mrtmath@gmail.com
Abstract: In this paper, we have introduced lacunary ideal convergence and condition of being
lacunary ideal Cauchy in fuzzy normed linear spaces and study some properties and relations of
these concepts.
Keywords: Lacunary Convergence, Statistical convergence, I-convergence, Fuzzy n-normed
space
References:
[1] H. Altınok, Y. Altın, and M. Et, Lacunary almost statistical convergence of fuzzy numbers, Thai
Journal of Mathematics, 2 (2) (2004), 265–274.
[2] J. A. Fridy and C. Orhan, Lacunary Statistical Convergence, Pasific Journal of Mathematics,
160 (1) (1993), 43–51.
[3] F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets
Systems, 99 (1998), 353–355.
[4] F. Nuray, U. Ulusu, and E. Dündar, Lacunary statistical convergence of double sequences of
sets, Soft Computing, 20 (7) (2016), 2883–2888.
[5] M. R. Türkmen and M. Çınar, Lacunary Statistical Convergence in Fuzzy Normed Linear
Spaces, Applied and Computational Mathematics, 6 (5) (2017), 233–237.
[6] M. R. Türkmen and H. Efe, On Some Properties Of Closability Of Farthest Point Maps in Fuzzy
n-Normed Spaces, imanager’s Journal on Mathematics, 2 (4) (2013), 33–38.
[7] M. R. Türkmen and E. Dündar, On lacunary statistical convergence of double sequences and
some properties in fuzzy normed spaces, Journal of Intelligent and Fuzzy Systems, DOI:10.
3233/JIFS-18841.
[8] L.A. Zadeh, Fuzzy sets, Information and Control 8(1965), 338-353.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
67
NEW TYPE SOFT SET AND MEDICAL DECION MAKING APPLICATION
Murat KİRİŞCİ
Department of Mathematical Education, Istanbul University-Cerrahpaşa, Fatih, 34470 Istanbul, Turkey,
mkirisci@hotmail.com
Abstract: In this study we apply new soft set theory for medical decion making. The problem is to
choose patient people with the variables used for Type II Diabetes Mellitus diagnosis. A comparison
matrix will be obtained for this selection and the maximum score will be reached with this matrix.
Keywords: soft set theory, decision making, comparison matrix.
References:
[1] M. Kirişci, H. Yılmaz, M. U. Saka, “An ANFIS perspective for the diagnosis of Type II Diabetes”,
(under communication)
[2] D. Molodtsov. " Soft Set Theory-First Results", Comput. Math. Appl. 37, (1999): 19-31.
[3] L.A: Zadeh. "Fuzzy Sets" Inf. Comp. 8, (1965): 338-353.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
68
REASONABLE MODIFICATIONS UNDER THE B-SPLINE BASIS WITH THE
SSPRK54 FOR SOLVING THE BURGERS EQUATION
Murat SARI, S. Ali-TAHIR
Yildiz Technical University, Department of Mathematics, Faculty of Arts and Science, 34220, Istanbul, Turkey,
sari@yildiz.edu.tr
shko.ali.tahir@std.yildiz.edu.tr
Abstract: In this work, we develop here a striking numerical method for solving the Burgers
equation. The numerical scheme is based on collocation of the modified cubic B-splines in the space
variable. The obtained results have been computed without using any linearization and
transformation processes. The produced diagonal system is solved by using the optimal strong
stability preserving time stepping Runge-Kutta for five stage and order four scheme (SSPRK54). The
present method is seen to be approximate for the advection dominant cases. The effectiveness of
this method is verified by considering some test problems for different values of the viscosity that can
be caused by the steep shock behavior. The numerical solutions are in good agreement with the
exact solutions and competent with those available in the literature. The present method is seen to
be relatively easy and economical implementation for researchers.
Keywords: cubic B-spline basis; Burgers equation; SSPRK54 method; CFL condition.
References:
[1] Boor C., A Practical Guide to Spline, Mathematics of Computation, 27, (1978).
[2] Schumaker L., Spline Functions, Basic Theory, Cambridge Mathematical Library, (2007)
[3] Schoenberg I. J., Contribution to the problem of approximation of equidistant data by analytic
functions, Quart. Appl.Math., 45-99, (1946)
[4] Morton K.W. and Mayers D.F., Numerical Solution of Partial Differential Equations?,
Cambridge university press, (1994)
[5] Mittal R.C.,Jain R.K., Numerical solution of nonlinear burgers equation with modified cubic B-
spline collocation method, Appl, math, comput, 218, 7839-7855, (2012)
[6] Dag I., irk D., Sahin A., B-Spline collocation methods for numerical solutions of the Burgers
equation, Math, Prob, 5, 521-538, (2005)
[7] Sari M., Gurarslan G. Numerical solutions of the generalized Burgers-Huxley equation by a
differential quadrature method. Mathematical 11: 370-765 (2009).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
69
NEW JUNGCK-TYPE ITERATIVE ALGORITHM AND NUMERICAL
RECKONING COINCIDENCE POINTS IN CONVEX METRIC SPACES
Musa DİKMEN1, Faik GÜRSOY2
1,2Department of Mathematics, Adiyaman University,02040 Adiyaman, Turkey,
musadikmen0202@gmail.com
faikgursoy02@hotmail.com
Abstract: In this presentation, we introduce a new Jungck-type iterative algorithm for a general class
of mappings and study its qualitative features like strong convergence, rate of convergence, stability
in convex metric spaces and data dependency in hyperbolic spaces. Validity of theoretical findings
obtained herein is shown through numerical examples. Our results are improvements and
generalizations of some recent results in the current literature.
Keywords: Almost contraction mappings, Jungck-type iterative algorithm, strong convergence, rate
of convergence, stability, data dependency.
References:
[1] Karakaya, V, Atalan, Y, Doğan, K, El Houda Bouzara, N, Some fixed point results for a new
three steps iteration process in Banach spaces, Fixed Point Theory 18, 625-640 (2017).
[2] F. Gürsoy, A. R. Khan, H. Fukhar-ud-din, Convergence and data dependence results for quasi-
contractive type operators in hyperbolic spaces, Hacet. J. Math. Stat. 46, 391-406 (2017).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
70
SOME FIXED POINT THEOREMS IN CONE METRIC SPACES OVER BANACH
ALGEBRAS
Muttalip ÖZAVŞAR
Department of Mathematics, Yildiz Technical University, Istanbul, Turkey
mozavsar@yildiz.edu.tr
Abstract: After Banach[1] introduced the contraction mapping principle in 1922, many researchers
extended his result to different contractive type mappings in the usual metric spaces and some
abstract spaces. For example, in 1989, Bakhtin [2] introduced b-metric space and then in 1993,
Czerwik [3] extended Banach’s principle to b-metric spaces. At the beginning of the 21 st century,
Berinde[4] presented the notion of (k,l)-almost contractions, which contains the classes of many
mappings such as Banach, Kannan and Chatterja type contractive mappings. Recently, Liu and Xu
[5] studied Banach’s contraction principle by using tools of spectral radius in the setting of cone metric
spaces over Banach algebra with a solid normal cone. Later, Xu and Radenovic [6] obtained the
results of [5] by omitting the normality condition for solid in underlying Banach algebra. In [7], the
fixed point theorem for (k,l)-almost contraction mappings is presented in the setting of cone metric
spaces over Banach algebras. In [8], Huang and Radenovic introduce some fixed point theorems
by introducing the notion of cone b-metric spaces over Banach algebras. In [9], George, Nabwey,
Rajagopalan, Radenovic and Reshma define the notion of cone b-metric with vector coefficient in
the setting of Banach algebra. In this talk we present the fixed point theorem for (k,l)-almost
contaction mappings in the setting of cone b-metric spaces with vector coefficient over Banach
Algebras.
References:
[1] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations
integrales, Fundamenta Mathematicae 3 (1922), 133–181.
[2] I. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. Unianowsk,
Gos. Ped. Inst. 30 (1989), 26–37.
[3] S. Czerwick, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica
Universitatis Ostraviensis 1 (1993), 5–11.
[4] V. Berinde, Approximating fixed points of weak contractions using the Picard iterations. Nonlinear
Anal. Forum. 9(2004), 43-53.
[5] H. Liu and S. Xu, Cone metric spaces with Banach algebras and fixed point theorems of
generalized Lipschitz mappings, Fix P Theory Appl. (2013), 10 pages.
[6] S. Xu and S. Radenovic, Fixed point theorems of generalized Lipschitz mappings on cone metric
spaces over Banach algebras without assumption of normality, Fix. P. Theory Appl. (2014), 12
pages.
[7] M.Özavşar, Fixed point theorems for (k,l)-almost contractions in cone metric spaces over Banach
algebras, Math.Adv.Pur.Appl.Sci. 1(2018), 46-51.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
71
ON FINITE DIMENSIONAL LEIBNIZ ALGEBRAS
Mücahit ÖZKAYA1, Nil MANSUROĞLU2
1,2Department of Mathematics, Kırşehir Ahi Evran University, 40100 Kırşehir, Turkey,
muco.ozk@icloud.com
nil.mansuroglu@ahievran.edu.tr
Abstract: In literature, firstly Leibniz algebras which are generalization of Lie algebras were
introduced as D-algebras by A.M. Bloh. Then, in 1993 these algebras which are called Leibniz
algebras were rediscovered by J.L. Loday. There are many researches on finite dimensional Leibniz
algebras. In this note, our main aim is to focus on finite dimensional Leibniz algebras and to give
some properties for the structure constants of Leibniz algebras.
Keywords: Lie algebra, Leibniz algebra, dimension, structure constant.
This work was supported by Kırşehir Ahi Evran University Scientific Research Projects Coordination
Unit. Project Number: FEF.A4.18.009.
References:
[1] Bloh, A.M. A generalization of the concept of Lie algebras, Dokl. Nauk. SSR, 165, 471-473
(1965)
[2] Demir, İ.; Kailash, C.M.; Stitzinger, E. On some structures of Leibniz algebras,
arXiv:1307.7672v1.
[3] Jacobson, N. Lie algebras, Dover, (1979)
[4] Loday, J.L. Une version non commutative des algebres de Lie: les algebres de Leibniz,
L'Enseignement Mathématique, 39, 269-293, (1993).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
72
CONVERGENCE AND STABILITY RESULTS FOR K* ITERATION
Müzeyyen ERTÜRK1, Faik GÜRSOY2, Vatan KARAKAYA3
1,2Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey,
merturk3263@gmail.com,
faikgursoy02@hotmail.com
3 Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210
Istanbul,Turkey,
vkkaya@yahoo.com
Abstract: In this presentation, we study convergence and stability results for K* iteration defined by
Ullah and Arshad [1] for a class mapping which includes the contractions. Also, we support our results
with the illustrative examples.
Keywords: K* iteration, convergence, stability
References:
[1] Ullah, K., and Arshad, M.: New three-step iteration process and fixed point approximation in
Banach spaces. Journal of Linear and Topological Algebra, 7.2, 87-100 (2018).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
73
A STUDY ON LATERAL BASES AND COVERED LATERAL IDEALS OF
ORDERED TERNARY SEMİGROUPS
M. Yahya ABBASI, Sabahat Ali KHAN and Aakif Fairooze TALEE
Department of Mathematics, Jamia Millia Islamia, New Delhi-110 025, India
mabbasi@jmi.ac.in
Abstract: In this paper, we define lateral bases and covered lateral ideals of ordered ternary
semigroups. Here we study their related properties and explore the relationship between lateral
base and covered lateral ideal of an ordered ternary semigroup.
Keywords: Ordered ternary semigroups, Lateral bases, Covered lateral ideals.
MSC(2010): 020M12, 20N99.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
74
APPROXIMATION PROPERTIES OF THE BERNSTEIN-CHLODOWSKY-
DURRMEYER OPERATORS ON THE WHOLE REEL AXIS
Nadire Fulda ODABAŞI1, Aydın İZGİ2
1,2Department of Mathematics, Harran University, Osmanbey Campus, Şanlıurfa, Turkey,
nadirefuldaodabasi@harran.edu.tr
aydinizgi@yahoo.com
Abstract: In this study, we introduced the Bernstein-Chlodowsky-Durrmeyer operators and
investigated some approximation properties of these operators. We obtained Korovkin type
approximation properties of these operators and estimated their rate of convergence by modulus of
continuity.
Keywords: Bernstein-Chlodowsky-Durrmeyer type operators, rate of convergence, modulus of
continuity.
References:
[1] Bernstein, S. N: Demonstration du theorem de Weierstrass fondee sur le calculu des
probabilites. Comp. Comm. Soc. Mat. Charkow. Ser., 13(2), 1-2 (1912).
[2] Chlodowsky, I: Sur le developpement des fonctions definies dans un intervalle infini en series
de polynomes de M. S. Bernstein. Compositio Math., 4, 380-393 (1937).
[3] Durrmeyer, J. L: Une formule d’inversion de la transformee de Laplace: applications a la
theorie des moments. These de 3e Cycle, Faculte des Sciences de I’Universite de Paris, 1967.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
75
ON 𝝀 𝝂-STATISTICAL CONVERGENCE OF ORDER 𝜶 OF GENERALIZED
DIFFERENCE SEQUENCES
Necip ŞİMŞEK1, Mikail ET2, Vatan KARAKAYA3
1Department of Mathematics, Graduate School of Applied and Natural Sciences, Istanbul Commerce
University, Küçükyalı Campus, Maltepe, Istanbul, Turkey,
nsimsek@ticaret.edu.tr
2Department of Mathematics, Fırat University, Elazığ, Turkey,
met@firat.edu.tr
3Department of Mathematical Engineering, Yıldız Technical University, Davutpaşa Campus, Esenler, Istanbul,
Turkey,
vkkaya@yahoo.com
Abstract: In this study we introduce the concepts 𝜆𝜈-statistical convergence and strong 𝜆𝜈-
summability of order of generalized difference sequences. Also some relations between 𝑆𝜆𝛼(𝛥𝜈
𝑚)-
statistical convergence and strong 𝑤𝜆𝛽(𝛥𝜈
𝑚 , 𝑝)-summability are given.
Keywords: Cesaro summability, difference sequence, Modulus function, statistical convergence.
References:
[1] Fast, H., “Sur la convergence statistique”, Colloq. Math., 1951, 2, 241-244.
[2] Schoenberg, I. J. “The integrability of certain functions and related summability methods”, Amer.
Math. Monthly, 1959, 66, 361-375.
[3] Connor, J. S. “The Statistical and strong p-Cesaro convergence of sequences”, Analysis, 1988,
8, 47-63.
[4] Edely, O. H. H. ; Mohiuddine, S. A. and Noman, A. K. “Korovkin type approximation theorems
obtained through generalized statistical convergence”, Appl. Math. Let., 2010, 23(11), 1382-1387.
[5] Et, M. ; Cinar, M. and Karakas, M. “On -statistical convergence of order of sequences of
function”, J. Inequal. Appl. 2013, 204, 8 pp.
[6] Fridy, J. “On statistical convergence”, Analysis, 1985, 5, 301-313.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
76
ON THE DEFORMATION OF SOME BANACH SEQUENCE SPACES
Necip ŞİMŞEK3, Ruken ÇELİK1, Zhamile ASKEROVA2,
1Department of Mathematics, Graduate School of Applied and Natural Sciences, Istanbul Commerce University,
Küçükyalı Campus, Maltepe, Istanbul, Turkey,
celik_ruken@hotmail.com
cemile05@mail.ru
nsimsek@ticaret.edu.tr
Abstract: In this paper using some moduli of convexity, moduli of smoothness and geometric
properties, we investigate the deformation of some Banach sequence spaces. We will calculate the
certain moduli of some certain sequence spaces and determine the modulus of deformation of the
sequence spaces.
Keywords: uniformly convex, uniformly smooth, modulus of convexity, modulus of smoothness.
References:
[1] J. Banas, K. Fraczek, Deformation Banach Spaces, Comment. Math. Univ. Carolin. 34(1)
(1993), 47--53.
[2] J. Banas, On moduli of Smoothness of Banach Spaces, Bull. Pol. Acad. Sci. Math. 34 (1986),
287--293.
[3] J. A., Clarkson, Uniformly Convex Spaces, Trans. Amer. Math. Soc. 40 (1936), 396--414.
[4] J. Alonso, A. Ullan, Moduli of Convexity, Functional Analysis and Approximation, edited by P.L.
Papini, Bagni di Lucca, Italy, May 16-20, (1988), 25--33.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
77
ON KRAWTCHOUK POLYNOMIALS
Nejla ÖZMEN
Department of Mathematics, Düzce University, Düzce, Turkey,
nejlaozmen06@gmail.com
Abstract: In this study deals with some new properties for the Krawtchouk polynomials. The results
obtained here include various families of multilinear and multilateral generating functions,
miscellaneous properties and also some special cases for these polynomials.
Keywords: generating function, summation formula, bilinear and bilateral generating function,
recurrence relations.
References:
[1] H. M. Srivastava and H.L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis
Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.
[2] N. Özmen and E. Erkus-Duman, Some families of generating functions for the generalized
Ces´aro polynomials, J. Comput. Anal. Appl., 25(4), 670-683 (2018).
[3] N. Özmen and E. Erkus-Duman, Some results for a family of multivariable polynomials, AIP
Conference Proceedings, 1558, 1124 (2013).
[4] P. Feinsilver and J. Kocik, Krawtchouk polynomials and Krawtchouk matrices, Recent
Advances in Applied Probability, 115-141(2005).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
78
ASYMPTOTICALLY LACUNARY I-INVARIANT EQUIVALENCE OF
SEQUENCES DEFINED BY A MODULUS FUNCTION
Nimet P. AKIN, Erdinç DÜNDAR and Uğur ULUSU
Department of Mathematics and Science Education, Afyon Kocatepe University, 03200, Afyonkarahisar,
Turkey
Department of Mathematics, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey,
npancaroglu@aku.edu.tr
edundar@aku.edu.tr
ulusu@aku.edu.tr
Abstract: In this paper, we introduce the concepts of strongly asymptotically lacunary ideal invariant
equivalence, f-asymptotically lacunary ideal invariant equivalence, strongly f-asymptotically lacunary
ideal invariant equivalence and asymptotically lacunary ideal invariant statistical equivalence for
sequences. Also, we investigate some relationships among them.
Keywords: Asymptotically equivalence, Lacunary invariant equivalence, I-equivalence, Modulus
function.
References:
[1] V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and
modulus function, Mathematical Sciences, 6(23)2012, 5-pages..
[2] P. Kostyrko, T. Salat and W. Wilczynski, I-Convergence, Real Anal. Exchange, 26(2) (2000),
669-686.
[3] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4) (1993), 755-
762.
[4] H. Nakano, Concave Modulars, J. Math. Soc.Japan, 5(1953), 29-49.
[5] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30(1)
(1963), 81-94.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
79
ASYMPTOTICALLY I-INVARIANT EQUIVALENCE OF SEQUENCES DEFINED
BY A MODULUS FUNCTION
Nimet P. AKIN, Erdinç DÜNDAR
Department of Mathematics and Science Education, Afyon Kocatepe University, 03200, Afyonkarahisar,
Turkey
Department of Mathematics, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey,
npancaroglu@aku.edu.tr
edundar@aku.edu.tr
Abstract: In this paper, we introduce the concepts of strongly asymptotically ideal invariant
equivalence, f-asymptotically ideal invariant equivalence, strongly f-asymptotically ideal invariant
equivalence and asymptotically ideal invariant statistical equivalence for sequences. Also, we
investigate some relationships among them.
Keywords: Asymptotically equivalence, Lacunary Invariant equivalence, I-equivalence, modulus
function.
References:
[1] V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and
modulus function, Mathematical Sciences, 6(23)2012, 5-pages.
[2] P. Kostyrko, T. Salat and W. Wilczynski, I-Convergence, Real Anal. Exchange, 26(2) (2000),
669-686.
[3] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4) (1993), 755-
762.
[4] H. Nakano, Concave Modulars, J. Math. Soc.Japan, 5(1953), 29-49.
[5] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30(1)
(1963), 81-94.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
80
ON FINITE DIMENSIONAL LEIBNIZ ALGEBRAS
Nil MANSUROĞLU1, Mücahit ÖZKAYA2
1,2Department of Mathematics, Kırşehir Ahi Evran University, 40100 Kırşehir, Turkey,
nil.mansuroglu@ahievran.edu.tr
muco.ozk@icloud.com
Abstract: In literature, firstly Leibniz algebras which are generalization of Lie algebras were
introduced as D-algebras by A.M. Bloh. Then, in 1993 these algebras which are called Leibniz
algebras were rediscovered by J.L. Loday. There are many researches on finite dimensional Leibniz
algebras. In this note, our main aim is to focus on finite dimensional Leibniz algebras and to give
some properties for the structure constants of Leibniz algebras.
Keywords: Lie algebra, Leibniz algebra, dimension, structure constant.
Acknowledgement: This work was supported by Kırşehir Ahi Evran University Scientific Research
Projects Coordination Unit. Project Number: FEF.A4.18.009.
References:
[1] Bloh, A.M. A generalization of the concept of Lie algebras, Dokl. Nauk. SSR, 165, 471-473
(1965)
[2] Demir, İ.; Kailash, C.M.; Stitzinger, E. On some structures of Leibniz algebras,
arXiv:1307.7672v1.
[3] Jacobson, N. Lie algebras, Dover, (1979)
[4] Loday, J.L. Une version non commutative des algebres de Lie: les algebres de Leibniz,
L'Enseignement Mathématique, 39, 269-293, (1993)
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
81
A NEW COMPLEX GENERALIZED BERNSTEIN-SCHURER OPERATOR
Nursel CETIN
Research Department, Turkish State Meteorological Service, Yenimahalle, 06560 Ankara, Turkey,
nurselcetin07@gmail.com
Abstract: In this paper, we consider the complex form of a new generalization of Bernstein-Schurer
operators and study some approximation properties. We obtain some quantitative estimates and the
exact order of approximation for these operators attached to analytic functions. Also, we prove that
these operators preserve some properties of the original function.
Keywords: complex Stancu operator, complex Bernstein-Schurer operator, quantitative estimates,
simultaneous approximation, exact order of approximation.
References:
[1] Stancu D.D., Quadrature formulas constructed by using certain linear positive operators,
Numerical Integration (Proc. Conf., Oberwolfach, 1981), ISNM 57 (1982) 241-251, Birkhäuser
Verlag, Basel.
[2] Gal S.G., Approximation by Complex Bernstein and Convolution Type Operators, Series on
Concrete and Applicable Mathematics, vol. 8, World Scientific Publishing Co., Pte. Ltd., Hackensack,
NJ, 2009.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
82
LACUNARY 𝑰𝟐-INVARIANT CONVERGENCE OF DOUBLE SEQUENCES OF
FUNCTIONS ON AMENABLE SEMIGROUP
Ömer KİŞİ1, Erhan GÜLER2
1,2Bartın University, Faculty of Science, Department of Mathematics, 74100 Bartın, Turkey
okisi@bartin.edu.tr
eguler@bartin.edu.tr
Abstract: In this study, the concept of lacunary invariant uniform density of any subset A of the set
N×N of double sequences of functions defined on discrete countable amenable semigroups is
defined. Associate with this, the concept of lacunary 𝐼2-invariant convergence for double sequences
of functions defined on discrete countable amenable semigroups is given. Also, we examine
relationships between this new type convergence concept and the concepts of lacunary invariant
convergence and p-strongly lacunary invariant convergence of double sequences of functions on
discrete countable amenable semigroups. Finally, introducing lacunary -invariant convergence
concept and lacunary 𝐼2∗-invariant Cauchy concepts of double sequences of functions on discrete
countable amenable semigroups, we give the relationships among these concepts and relationships
with lacunary 𝐼2-invariant convergence concept.
Keywords: lacunary, Ideal, I-Convergence, Double Sequences of Functions, double sequence,
invariant.
References:
[1] E. Dündar, U. Ulusu and F. Nuray, On ideal invariant convergence of double sequences and
some properties, Creat. Math. Inf., 27(2) (2018).
[2] E. Dündar and B. Altay, 𝐼2-convergence and 𝐼2-Cauchy of double sequences, Acta Math. Sci.,
34B(2) (2014), 343-353.
[3] P.Das, P.Kostyrko, W.Wilczynski, P.Malik, I and 𝐼∗-convergence of double sequences, Math.
Slovaca, 58(5) (2008) 605-620.
[4] U. Ulusu, E. Dündar, F. Nuray, Lacunary 𝐼2-Invariant Convergence and some properties,
International Journal of Analysis and Applications Volume 16, Number 3 (2018), 317-327.
[5] M. Day, Amenable semigroups, Illinois J. Math. 1 (1957) 509–544.
[6] S.A. Douglass, On a concept of summability in amenable semigroups, Math. Scand. 28 (1968)
96-102.
[7] Nuray F., Rhoades B.E., Some kinds of convergence defined by Folner sequences, Analysis
31(4) (2011) 381–390.
[8] Nuray F., Rhoades B.E., Asymptotically and Statistically Equivalent Functions Defined on
Amenable Semigroups, Thai Journal of Mathematics, Volume 11(2) (2013) 303–311.
[9] I. Nomika, Folner’s conditions for amenable semigroups, Math. Scand. 15 (1964) 18–28.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
83
A GENERALIZED STATISTICAL CONVERGENCE VIA IDEALS DEFINED BY
FOLNER SEQUENCE ON AMENABLE SEMIGROUPS
Ömer KİŞİ1, Erhan GÜLER2
1,2Bartın University, Faculty of Science, Department of Mathematics, 74100 Bartın, Turkey
okisi@bartin.edu.tr
eguler@bartin.edu.tr
Abstract: The purpose of this study is to extend the notions of I-convergence, I-limit superior and I-
limit inferior, I-cluster point and I-limit point to functions defined on discrete countable amenable
semigroups. Also, in this paper, we make a new approach to the notions of [V,λ]-summability and λ-
statistical convergence by using ideals and introduce new notions, namely, I-[V,λ]-summability and
I,λ-statistical convergence to functions defined on discrete countable amenable semigroups.
Keywords: inferior, superior, I-Convergence, folner sequence, amenable semigroup.
References:
[1] P. P. Kostyrko, T. Salát, W. Wilezyński, I-Convergence, Real Analysis Exchange Vol. 26(2), pp.
669-686 (2000/2001).
[2] K. Demirci, I-limit superior and limit inferior, Math. Commun. 6 (2001), no. 2, 165--172.
[3] M. Day, Amenable semigroups, Illinois J. Math.1 (1957) 509–544.
[4] S.A. Douglass, On a concept of summability in amenable semigroups, Math. Scand. 28 (1968)
96-102.
[5] Nuray F., Rhoades B.E., Some kinds of convergence defined by Folner sequences, Analysis
31(4) (2011) 381–390.
[6] Nuray F., Rhoades B.E., Asymptotically and Statistically Equivalent Functions Defined on
Amenable Semigroups, Thai Journal of Mathematics, Volume 11(2) (2013) 303–311.
[7] I. Nomika, Folner’s conditions for amenable semigroups, Math. Scand. 15 (1964) 18–28.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
84
ON THE NEW SOLUTIONS OF (3+1)-DIMENSIONAL POTENTIAL-YTSF
EQUATION BY 𝒕𝒂𝒏(𝑭(𝝃) 𝟐⁄ )-EXPANSION METHOD
Ozlem KIRCI1, Hasan BULUT2
1Department of Mathematics, Kirklareli University, Kayali Campus, 39000, Kirklareli, Turkey,
ozlem.isik@klu.edu.tr
2 Department of Mathematics, Firat University, 23200, Elazig, Turkey,
hbulut@firat.edu.tr
Abstract: In this paper, we employ the 𝑡𝑎𝑛(𝐹(𝜉) 2⁄ )-expansion method to explore the solution
structure of the (3+1)-dimensional potential-YTSF equation. We obtain new solitary wave solutions
in the form of trigonometric function, hyperbolic function, exponential function and rational function.
We also plot two- and three-dimensional graphics of some obtained solutions. In this study, all
computations are performed with the aid of Mathematica 9 and consequently a comprehensive
conclusion is submitted.
Keywords: The 𝒕𝒂𝒏(𝑭(𝝃) 𝟐⁄ )-expansion method, the (3+1)-dimensional potential-YTSF equation,
trigonometric function solutions, hyperbolic function solutions, exponential function solutions, rational
function solutions.
References:
[1] Bulut, H, Sulaiman, T.A., Baskonus H.M.: New Solitary and Optical Wave Structures to the
Korteweg-de Vries Equation with Dual-Power Law Nonlinearity. Opt. Quant. Electron 48 (564), 1-14
(2016)
[2] Kadkhoda N: Exact Solutions of (3+1)-Dimensional Nonlinear Evolution Equations. Caspian
Journal of Mathematical Sciences 4 (2), 189-195 (2015)
[3] Manafian, J: Optical Soliton Solutions for Schrodinger Type Nonlinear Evolution Equations
the 𝑡𝑎𝑛(𝐹(𝜉) 2⁄ )-Expansion Method. Optik- International Journal of Light and Electron Optics 127
(10), 4222-4245 (2016)
[4] Wang, Y-P: Solving the (3+1)-Dimensional Potential-YTSF Equation with Exp-function Method.
Journal of Physics 96, 012186 (2008)
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
85
CONVERGENCE OF THE INVERSE CONTINUOUS WAVELET TRANSFORM IN
WEIGHTED VARIABLE EXPONENT AMALGAM SPACES
Öznur KULAK1, İsmail AYDIN2
1Department of Banking and Finance, Giresun University, Görele, Giresun, Turkey,
oznur.kulak@giresun.edu.tr
2 Department of Mathematics, Sinop University, Sinop, Turkey,
iaydın@sinop.edu.tr
Abstract: In this study, we present the some basic properties of the weighted variable exponent
amalgam spaces and investigate the θ-means of f converge to f almost everywhere and in norm for
all f in these spaces under which conditions. Later using these results, we consider norm and almost
everywhere convergence of the inverse continuous wavelet transform in these spaces.
Keywords: weighted variable exponent amalgam spaces, inverse continuous wavelet transform, θ-
summability.
References:
[1] Szarvas, K., Weisz, F. (2014). Continuous Wavelet Transform in Variable Lebesgue Spaces,
Stud. Univ. Babeş-Bolyai Math., 59(4), 497-512.
[2] Weisz, F., (2015). Convergence of the Continuous Wavelet Transform in Winer Amalgam Spaces, De Gruyter, 35(1), 33-46.
[3] Aydın, İ., Gürkanlı, A. T., (2012). Weighted Variable Exponent Amalgam Spaces W(L^p(x)
,L_m^q), Glasnik Matematicki, 47867), 165-174.
[4] Szarvas, K., (2016). Variable Lebesgue Spaces and Continuous Wavelet Transforms, Acta
Mathematica Academiae Paedagogicae Nyiregyhaziensis, 32, 313-325.
[5] Cruz-Uribe, D. V., Fiorenza, A., (2013). Variable Lebesgue Spaces, Foundations and Harmonic
Analysis, New York, NY: Birkhauser/Springer.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
86
A NEW OPERATOR IDEAL ON BLOCK SEQUENCE SPACES
Pınar ZENGİN ALP1, Emrah Evren KARA2
1,2Department of Mathematics, Düzce University, Konuralp Campus Düzce, Turkey,
pinarzengin13@gmail.com
karaeevren@gmail.com
Abstract: In this study, we define a new operator ideal on block sequence spaces. Also we give a
quasi-norm on this ideal and show that this class is a quasi-Banach operator ideal.
Keywords: quasi-norm, operator ideal, block sequence space.
References:
[1] D. Foroutannia, On the block sequence space lp (E) and related matrix transformations, Turk J.
Math., (39), 830-841 (2015)
[2] A. Maji, P.D. Srivastava, Some class of operator ideals, Int. J. Pure Appl. Math., 83 (5),731-740
(2013)
[3] A. Pietsch, Operator Ideals, VEB Deutscher Verlag der Wissenschaften, Berlin (1978).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
87
ON BICOMPLEX JACOBSTHAL-LUCAS NUMBERS
Serpil HALICI1*, Sevim ASLAN2
1Department of Mathematics, Pamukkale University, Denizli, Turkey
shalici@pau.edu.tr
aslansevim121@gmail.com
Abstract: In this study, we defined a sequence of bicomplex numbers with coefficients from the
Jacobsthal-Lucas sequence. We investigated some fundamental properties of this new sequence.
Moreover, thanks to the recursive relation that these numbers are, we gave many important
identities.
Keywords: Recurrences; Jacobsthal numbers; bicomplex numbers
Mathematics Subject Classification(2010): 11B37, 11B39, 11B83.
References:
[1] Aydın, T. Bicomplex Fibonacci quaternions. Chaos, Solitons & Fractals, 106(2018),147-153.
[2] Bagchi, B., & A. Banerjee, Bicomplex hamiltonian systems in quantum mechanics. Journal of
Physics A: Mathematical and Theoretical 48(50)(2015) (503001-505402).
[3] Cerin, Z. Sums of Squares and Products of Jacobsthal Numbers, Journal of Integer Sequence
10(2007) Article 07.2.5.
[4] Cockle J, On Systems of Algebra Involving more than one Imaginary, Philosophical Magazine
(series 3) 35 (1849) 434-435.
[5] Djordjevic G. B., Derivative Sequence of Generalized Jacobsthal and Jacobsthal-Lucas
Polynomials, The Fibonacci Quarterly 38(2000) 334-338.
[6] Djordjevic G. B., Generalized Jacobsthal Polynomials, The Fibonacci Quarterly 38(2009) 239-
243.
[7] Flaut, C., & Savin D. Quaternion algebras and generalized Fibonacci Lucas quaternions.
Advances in Applied Clifford Algebras 25(4) (2015) 853-862.
[8] Halici, S. , On Fibonacci quaternions, Adv. in App. Clifford Alg. 22(2) (2012), 321-327.
[9] Halici, S. On complex Fibonacci quaternions. Advances in applied Clifford algebras, 23(1) (2013),
105-112.
[10] Hamilton, W. R. LXXVIII. On quaternions; or on a new system of imaginaries in Algebra: To the
editors of the Philosophical Magazine and Journal. Philosophical Magazine Series 3, 25(169) (1844)
489-495.
[11] Horadam, A. F. Complex Fibonacci numbers and Fibonacci quaternions. The American
Mathematical Monthly, 70(3) (1963), 289-291.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
88
ALGEBRA OF CONVERGENCE SET SEQUENCE
Sibel ÖZTÜRK1 and Harun POLAT2
1,2Muş Alparslan University Art and Science Faculty, Department of Mathematics, 49100 Muş,Turkey.
Sibelozturk91@windowslive.com, h.polat@alparlan.edu.tr
Abstract: There are different convergence notions for sequence of sets, which have significance for
certain applications. Kuratowski convergence, Hausdorff convergence, Wijsman convergence,
Fisher convergence and Mosco convergence are the best known types of convergence. In this study,
we examine algebra of these types of convergent set sequences. Also we characterize the
connections between of their.
Keywords: Kuratowski, Hausdorff, Wijsman, Fisher and Mosco convergence, algebra.
References:
[1] C. Kuratowski, Topology, Academic Press, New York, 1966.
[2] F. Hausdorff , Grundzuge derMengenlehre, Verlag von Veit, Leipzig, Reprinted by Chelsea, New
York1914.
[3] R. A. Wijsman,” Convergence of sequences of convex sets, cones and functions”, Bull. Amer.
Math. Soc. 70 (1964) 186-188.
[4] B. Fisher, “Common fixed points of mappings and set-valued mappings”, Rostock Math. Kolloq.
18 (1981) 69-77.
[5] U. Mosco, “Convergence of convex sets and of solutions of variational inequalities”, Adv. in Math.
3 (1969), 510-585.
[6] M. Baronti, P. Papini, (1986) Convergence of sequences of sets, Methods of functional analysis
in approximation theory, ISNM 76,Birkhauser, Basel.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
89
RESULTS ON A CLASS OF HARMONIC UNIVALENT FUNCTIONS INVOLVING
A NEW DIFFERENTIAL OPERATOR
Sibel YALÇIN TOKGÖZ1, Şahsene ALTINKAYA2
1,2Department of Mathematics, Bursa Uludag University, Faculty of Arts and Sciences, 16059 Bursa, Turkey,
syalcin@uludag.edu.tr
sahsene@uludag.edu.tr
Abstract: In this paper, a new subclass of complex-valued harmonic univalent functions involving a
new differential operator is introduced. We investigate necessary and sufficient coefficient bounds,
distortion inequalities, extreme points and inclusion results for this class.
Keywords: harmonic functions, univalent functions, starlike and convex functions, differential
operator.
References:
[1] Altınkaya, Ş and Yalçın, S: On a class of Harmonic univalent functions defined by using a new
differential operator. Theory Appl. Math. Comput. Sci. 6.2 (2016) 125-133.
[2] Bucur, R., L. Andrei and D. Daniel: Coefficient bounds and Fekete-Szegö problem for a class of
analytic functions defined by using a new differential operator. Appl. Math. Sci. 9, 1355–1368. (2015)
[3] Clunie, J, Sheil-Small, T: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. AI Math. 9
(1984) 3-25.
[4] Duren, P.: Harmonic Mappings in the Plane. CRC Press: Cambridge Tracts in Mathematics,
Cambridge University Press (2004).
[5] Jahangiri, J M, Murugusundaramoorthy G and Vijaya, K: Salagean-type harmonic univalent
functions. South J. Pure Appl. Math. 2 (2002) 77-82.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
90
CERTAIN CONVEX HARMONIC FUNCTIONS DEFINED BY SUBORDINATION
Sibel YALÇIN TOKGÖZ1, Şahsene ALTINKAYA2
1,2Department of Mathematics, Bursa Uludag University, Faculty of Arts and Sciences, 16059 Bursa, Turkey,
syalcin@uludag.edu.tr
sahsene@uludag.edu.tr
Abstract: We investigate certain subclass of convex harmonic univalent functions defined by
subordination. We obtain coefficient bounds, distortion theorems, extreme points, convolution and
convex combinations for this class of functions.
Keywords: harmonic functions, univalent functions, convex functions, subordination.
References:
[1] Clunie, J, Sheil-Small, T: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. AI Math. 9,
3-25 (1984)
[2] Dziok, J: Classes of harmonic functions defined by subordination. Abstr. Appl. Anal.
2015.756928 (2015) 1-9.
[3] Kim, Y C, Jahangiri, J M, Choi, J H: Certain convex harmonic functions. Int. J. Math. Math. Sci.
29.8 (2002) 459-465.
[4] Silverman, H: Harmonic univalent functions with negative coefficients. J. Math. Anal. Appl. 220,
283-289 (1998).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
91
CERTAIN SUBCLASSES OF HARMONIC UNIVALENT FUNCTIONS
ASSOCIATED WITH A MULTIPLIER LINEAR OPERATOR
Sibel YALÇIN TOKGÖZ1, Şahsene ALTINKAYA2
1,2Department of Mathematics, Bursa Uludag University, Faculty of Arts and Sciences, 16059 Bursa, Turkey,
syalcin@uludag.edu.tr
sahsene@uludag.edu.tr
Abstract: In the paper, we introduce new subclasses of functions defined by multiplier differential
operator and give coefficient bounds for these subclasses. Also, we obtain necessary and sufficient
convolution conditions, distortion bounds and extreme points for these subclasses of functions.
Keywords: harmonic functions, univalent functions, multiplier transformation, subordination,
modified differential operator.
References:
[1] Altınkaya, Ş and Yalçın, S: On a class of Harmonic univalent functions defined by using a new
differential operator. Theory Appl. Math. Comput. Sci. 6.2 (2016) 125-133.
[2] Clunie, J, Sheil-Small, T: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. AI Math. 9,
3-25 (1984)
[3] Dziok, J: Classes of harmonic functions defined by subordination. Abstr. Appl. Anal.
2015.756928 (2015) 1-9.
[4] Jahangiri, J M, Murugusundaramoorthy G and Vijaya, K: Salagean-type harmonic univalent
functions. South J. Pure Appl. Math. 2, 77-82 (2002).
[5] Yaşar, E and Yalçın, S: Generalized Salagean-type harmonic univalent functions. Stud. Univ.
Babeş-Bolyai Math. 57. 3, 395-403 (2012).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
92
An h-DEFORMATION OF SYMPLECTIC (1+2)-SUPERSPACE VIA A
CONTRACTION
Sultan Abaci CELIK1, Canan AYDEMIR2
1,2Department of Mathematics, Yildiz Technical University, Davutpasa Campus, Esenler, 34220 Istanbul,
Turkey,
sultan@yildiz.edu.tr
cnanaydemr.94@gmail.com
Abstract: In this study, we introduce an h-deformation of the symplectic superspace 𝑆𝑃1|2 from the
q-deformation via a contraction following the method of [1]. Here we denote q-deformed objects by
primed quantities. Unprimed quantities represent transformed coordinates. We consider the q-
deformed algebra of functions on the quantum symplectic superspace 1|2
qSP generated by 𝜉′, 𝑥′and
𝜂′ with the relations [2]
𝑥′𝜉′ = 𝑞𝜉′𝑥′ , 𝑥′𝜂′ = 𝑞−1𝜂′𝑥′, 𝜂′𝜉′ = −𝑞2𝜉′𝜂′ + 𝑞1/2(1 − 𝑞)𝑥′2 , 𝜉′2 = 0 = 𝜂′2
and we introduce new coordinates , x and with the change of basis in the coordinates of the q-
superspace using the following matrix g [3]:
𝑋′ = (𝜉′
𝑥′
𝜂′
) = (1 0 00 1 0ℎ′ 0 1
) (𝜉𝑥𝜂
) = 𝑔𝑋, ℎ′ =ℎ
2(𝑞 − 1)
Here h is a new deformation parameter that will be replaced by q when 𝑞 → 1.
Keywords: symplectic superspace, q-deformation, h-deformation.
References:
[1] Aghamohammadi, A, Khorrami, M and Shariati, A, h-deformation as a contraction of q-
deformation, J. Phys. A: Math. Gen. 28 (1995): L225-L231.
[2] Aizawa, N, and Chakrabarti, R, Quantum Spheres for (1| 2)qSP , J. Math. Phys. 46
(2005).:103510-1-12.
[3] Celik, S, Covariant differential calculi on quantum symplectic superspace 1|2
qSP , J. Math. Phys.
58 (2017): 023508-1-15.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
93
ON A SUBCLASS OF BI-UNIVALENT FUNCTIONS WITH THE FABER
POLYNOMIAL EXPANSIONS
Şahsene ALTINKAYA1, Sibel YALÇIN2
1,2Department of Mathematics, Uludag University, 16059 Bursa, Turkey,
sahsene@uludag.edu.tr
syalcin@uludag.edu.tr
Abstract: In this study, we use the Faber polynomial expansions to obtain upper bounds for
|𝑎𝑛|(𝑛 > 3) coefficients of functions belong to a subclass of bi-univalent functions involving the
Jackson (p,q)-derivative operator in the open unit disc
𝔻 = {𝑧 ∈ ℂ: |𝑧| < 1}.
Keywords: Bi-univalent functions, Faber polynomials, coefficient bounds, quasi-subordination.
References:
[1] Airault, H, and Bouali, H. “Differential calculus on the Faber polynomials.” Bulletin des Sciences
Mathematiques, (2006): 179-222.
[2] Airault, H. “Remarks on Faber polynomials.” Int. Math. Forum 3. (2008): 449-456.
[3] Altınkaya, Ş, and Yalçın, S. “Faber polynomial coefficient estimates for Bi- univalent functions
of complex order based on subordinate conditions involving of the Jackson (p,q)-derivative.”
Miskolc Mathematical Notes 18.(2017): 555-572.
[4] Chakrabarti, R, and Jagannathan, R. “A (p,q)-oscillator realization of two-parameter quantum
algebras.” J. Phys. A: Math. Gen 24. (1991): L711–L718.
[5] P. Duren, Univalent Functions, New York: Grundlehren der Mathematischen Wissenschaften,
Springer, 1983.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
94
CHEBYSHEV POLYNOMIAL COEFFICIENT RESULTS ON A SUBCLASS OF
ANALYTIC AND BI-UNIVALENT FUNCTIONS INVOLVING QUASI-
SUBORDINATION
Şahsene ALTINKAYA1, Sibel YALÇIN2
1,2Department of Mathematics, Uludag University, 16059 Bursa, Turkey,
sahsene@uludag.edu.tr
syalcin@uludag.edu.tr
Abstract: In this study, we use the Chebyshev polynomial expansion to construct a new subclass of
bi-univalent functions involving quasi-subordination.
Keywords: Chebyshev polynomials, coefficient bounds, quasi-subordination.
References:
[1] Altınkaya, Ş, and Yalçın, S. “On the Chebyshev polynomial bounds for classes of univalent
functions.” Khayyam Journal of Mathematics 2. (2016): 1-5.
[2] Doha, E. H. “The first and second kind Chebyshev coefficients of the moments of the general-
order derivative of an infinitely differentiable function.” Intern. J. Comput. Math. 51. (1994): 21-35.
[3] Dziok, J, Raina, R. K., and Sokol, J. “Application of Chebyshev polynomials to classes of analytic
functions.” C. R. Acad. Sci. Paris 353. (2015): 433-438.
[4] Z. Nehari, Conformal Mappings, McGraw-Hill, New York, 1952.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
95
ON THE BOUNDS OF GENERAL SUBCLASSES OF ANALYTIC AND BI-
UNIVALENT FUNCTIONS ASSOCIATED WITH SUBORDINATION
Şahsene ALTINKAYA1, Sibel YALÇIN2
1,2Department of Mathematics, Uludag University, 16059 Bursa, Turkey,
sahsene@uludag.edu.tr
syalcin@uludag.edu.tr
Abstract: In this study, we define several new subclasses of bi-univalent functions involving a
differential operator in the open unit disc
𝔻 = {𝑧 ∈ ℂ: |𝑧| < 1}.
Moreover, we obtain estimates on the coefficients for functions belonging to these classes.
Keywords: Bi-univalent functions, coefficient bounds, subordination.
References:
[1] Amourah, A, and Darus, M. “Some properties of a new class of univalent functions involving a
new generalized differential operator with negative coefficients.” Indian Journal of Science and
Technology 9. (2016): 1-7.
[2] Brannan, D. A, and Taha, T. S. “On some classes of bi-univalent functions.” Studia Universitatis
Babeş-Bolyai Mathematica 31. (1986): 70-77.
[3] P. Duren, Univalent Functions, New York: Grundlehren der Mathematischen Wissenschaften,
Springer, 1983.
[4] Ch. Pommerenke, Univalent functions, Vandenhoeck and Rupercht, Göttingen, 1975.
[5] Lewin, M. “On a coefficient problem for bi-univalent functions.” Proc. Amer. Math. Soc. 18.
(1967): 63-68.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
96
STATISTICAL CONVERGENCE OF MINIMA AND MINIMIZERS OF
SEQUENCES OF FUNCTIONS
Şükrü TORTOP1, Yurdal SEVER1 and ÖZER TALO2
1Department of Mathematics, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey
2 Yenimahalle, Yunusemre, Manisa, Turkey
stortop@aku.edu.tr
ysever@aku.edu.tr
ozertalo@hotmail.com
Abstract: In this paper, we show that, under some statistical level boundedness assumptions,
statistical epi-convergence of a sequence (fn) to a function f implies the statistical convergence of the
minimum values of (fn) to the minimum value of f. Furthermore, in case (fn) and f have a unique
minimum point, we shall prove that the sequence of the minimizers of (fn) statistically converges to
the minimizer of f.
Keywords: statistical epi-convergence, statistical level boundedness, epigraphs, lower semi
continuity.
References:
[1] Fast, H.: Sur la convergence statistique. Colloq. Math. 2 241-244 (1951)
[2] Fridy, J. A.: Statistical limit points. Proc. Amer. Math. Soc. 118 (4) 1182-1192 (1993)
[3] Fridy, J. A., Orhan, C.: Statistical limit superior and limit inferior. Proc. Amer. Math. Soc. 125
3625-3631 (1997)
[4] Maso, G. D.: An introduction to Γ-convergence, vol.8. Boston (1993)
[5] Wets, R.J-B.: Convergence of convex functions, variational inequalities and convex optimization
problems. New York (1980)
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
97
ON THE σ-STABLE FAMILIES
Taner BÜYÜKKÖROĞLU1, Özlem ESEN2, Vakıf CAFER3
1,3Department of Mathematics, Eskişehir Technical University, Yunusemre Campus, 26470, Eskişehir, Turkey,
tbuyukkoroglu@anadolu.edu.tr
vcaferov@anadolu.edu.tr
2School for the Handicapped, Anadolu University, Yunusemre Campus,26470, Eskişehir, Turkey,
oavul@anadolu.edu.tr
Abstract: Given a positive number σ, the set of all complex numbers with real parts less than –σ, is
called σ-shifted Hurwitz stability region. For a linear system if all roots of the characteristic polynomial
belong to a shifted region, the system is said to be σ-stable. This property is very important in the
investigation of performance and stability problems. In this report we consider σ-stability problem for
uncertain linear systems. For an interval family, we find the largest value of σ for which the interval
family is stable. We establish sufficient conditions for segment stability which is important for the
application of the Edge theorem.
Keywords: shifted region, interval family, maximal stability region, segment stability.
References:
[1] Bhattacharyya , S.P., Chapellat, H., Keel, L.H., Robust Control: The Parametric Approach, New
Jersey, Prentice-Hall, 1995.
[2] Kawabata, K., Mori, T., Kuroe, Y., Directional Stability Radius: A Stability Analysis Tool for
Uncertain Polynomial Systems, IEEE Transactions on Automatic Control, vol. 48(6), 1012-1016
(2003).
[3] Matsuda, T., Derivation of Robust Stability Ranges for Disconnected Region with Multiple
Parameters, SICE Journal of Control, Measurement, and System Integration, Vol. 10, No. 1, pp. 032–
038 (2017).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
98
ON SOME ASYMPTOTICALLY EQUIVALENCE TYPES FOR DOUBLE
SEQUENCES AND RELATIONS AMONG THEM
Uğur ULUSU, Erdinç DÜNDAR
Department of Mathematics, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey,
ulusu@aku.edu.tr
edundar@aku.edu.tr
Abstract: In this study, we give definitions of asymptotically lacunary invariant equivalence, strongly
asymptotically lacunary invariant equivalence and asymptotically lacunary ideal invariant
equivalence for double sequences. We also examine the existence of some relations among these
new equivalence definitions.
Keywords: asymptotically equivalence, double sequence, ideal convergence, invariant
convergence, double lacunary sequence.
References:
[1] B. Hazarika, V. Kumar, On asymptotically double lacunary statistical equivalent sequences in
ideal context, Journal of Inequalities and Applications, 2013:543 (2013), 1-15.
[2] P. Kostyrko, T. Salat and W. Wilczynski, I-Convergence, Real Anal. Exchange, 26(2) (2000),
669-686.
[3] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4) (1993), 755-
762.
[4] A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53(3) (1900),
289-321.
[5] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30(1)
(1963), 81-94.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
99
STATISTICAL LACUNARY INVARIANT SUMMABILITY OF DOUBLE
SEQUENCES
Uğur ULUSU, Esra GÜLLE
Department of Mathematics, Afyon Kocatepe University, 03200, Afyonkarahisar, Turkey,
ulusu@aku.edu.tr
egulle@aku.edu.tr
Abstract: In this study, we give definitions of lacunary -summability, strongly p-lacunary -
summability and statistical lacunary -summability for double sequences. We also examine the
existence of some relations among the definitions of statistical lacunary -summability, lacunary
invariant statistical convergence and strongly p-lacunary -convergence.
Keywords: statistical convergence, double lacunary sequence, invariant convergence, double
sequence.
References:
[1] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
[2] S. A. Mohiuddine and E. Savaş, Lacunary statistically convergent double sequences in
probabilistic normed spaces, Ann Univ. Ferrara, 58 (2012), 331-339.
[3] A. Pringsheim, Zur theorie der zweifach unendlichen Zahlenfolgen, Math. Ann. 53(3) (1900),
289-321.
[4] R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30(1)
(1963), 81-94.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
100
REDUCTION OF NAVIER-STOKES EQUATION TO A LINEAR EQUATION
Waleed KHEDR
Independent Researcher, Cairo, Egypt
waleedshawki@yahoo.com
Abstract: In this article, we provide two theorems on pointwise coincidence between solutions of
Navier-Stokes equation and solutions of standard linear second order parabolic equations with the
same data. We show that the convection, the pressure, and the external forces (if applied) are
governed by some sort of balance independent of the equation that governs the solution itself. In
light of the well establishment of the theory of existence, regularity and uniqueness of linear second
order parabolic equations, this result represents an important step to fully understand the qualitative
properties of the solutions to Navier-Stokes equation.
Conclusion: In the presence of an 𝐿𝑞 external force 𝑓 = 𝑔 + 𝑘 where 𝑔 = 𝛻𝜙 and𝑘 k are the
components of the Helmholtz-Weyl decomposition, initial profile 𝑣0 ∈ 𝑊1,2(𝛺) and 𝛻 ⋅ 𝑣0 = 0,
and boundary datum 𝑣 ∈ 𝑊1,2(𝜕𝛺) if 𝛺 is bounded ; the following conclusion follows. In arbitrary
domain, Navier-Stokes equation is reduced to a linear parabolic model:
( )
−
−
Ωatv=v
atΩv=v
vatΩvg=p
atΩ=vk,=μΔvv
t
tt
ˆ
0
00
Keywords: Fluid Mechanics, Navier-Stokes equation, Convection
Acknowledgement: This is the abstract of the article submitted to arXiv on 24th of January 2018
with submission number arXiv: submit/2142016.
References:
[1] J. Leray, Etude de diverses equations integrales non lineaires et de quelques problemes que
pose lhydrodynamique, J. Math. Pures Appl., 12, 1933, 1-82.
[2] J. Leray, Essai sur les mouvements plans d'un liquide visqueux que limitent des parois, J.
Math. Pures Appl., 13, 1934, 341-418.
[3] J. Leray, Essai sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math., 63,
1934, 193-248.
[4] W. S. Khedr, Classical fundamental unique solution for the incompressible Navier-Stokes
equation in RN, Jamp, 5, 939-952, 2017.
[5] W. S. Khedr, Nonconvection and uniqueness in Navier-Stokes equation, arXiv:1706.02552,
2017.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
101
EXTENDED KRYLOV METHOD FOR THE NUMERICAL RESOLUTION OF A
LARGE SCALE DIFFERENTIAL SYMMETRIC STEIN EQUATIONS
Yaprak DERICIOGLU1 and Muhammet KURULAY2
1Department of Mathematics, Yildiz Technical University, Istanbul,34220, Turkey
guldogan@yildiz.edu.tr
2Department of Mathematical Engineering, Yildiz Technical University, Istanbul, 34220, Turkey
Abstract: In this study, we consider large-scale differential symmetric Stein equations. These matrix
equations have many applications in filtering and image restorations. Our aim is to propose an
iterative method for solution of this problem. The initial problem is projected on a Krylov subspace
then solved by an integration method. We give some numerical examples and theoritical results to
show effectiveness of our method.
Keywords: Large scale systems, Extended Krylov method, Projection methods, Differential
Symmetric Stein equations
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
102
ON A NEW ESCAPE CRITERIONS FOR COMPLEX POLYNOMIALS USING
FIXED POINT ITERATION METHOD AND S-CONVEXITY
Yunus ATALAN1, Vatan KARAKAYA2
1Department of Mathematics, Aksaray University, Campus, 68100 Aksaray, Turkey,
yunusatalan@aksaray.edu.tr
2 Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210
Istanbul,Turkey,
vkkaya@yahoo.com
Abstract: The purpose of this work is to obtain some fixed point results in the generation of fractals
using S*-iteration method with s-convexity for quadratic, cubic and n-th degree polynomials..
Keywords: fractals, fixed point iteration, s-convexity.
References:
[1] Cho, S. Y., Shahid, A. A., Nazeer, W., & Kang, S. M.. “Fixed point results for
fractal generation in Noor orbit and s-convexity”. Springer Plus, 5(1), (2016): 1-16.
[2] Kumari, M. Ashish and R. Chugh, “New Julia And Mandelbrot Sets for a New Faster
Iterative Process”. International Journal of Pure and Applied Mathematics, 107(1), (2016): 161-177.
[3] Partap, N., and Chugh, R.. “Fixed Point Iterative Techniques–An Application to Fractals”. International Journal of Research in Mathematics & Computation. 4(1), (2016): 1-7.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
103
A NEW ITERATION METHOD AND SOME FIXED POINT RESULTS
Yunus ATALAN
Department of Mathematics, Aksaray University, 68100, Aksaray, Turkey,
yunusatalan@aksaray.edu.tr
Abstract: In this work, we introduced a new iteration method using almost contraction mappings.
We obtain strong converngence and rate of convergence results for this method. Also we give a data
dependence result for almost contraction mappings by using the new iteration method.
Keywords: new iteration, strong convergence, rate of convergence, data dependence.
References:
[1] Karakaya, V, Atalan,Y, Dogan, K. and Bouzara, NEH.” Some Fixed Point Results For a New
Three Steps Iteration Process in Banach Spaces”.Fixed Point Theory 18(2), 625-640 (2017)
[2] V. Berinde, Iterative Approximation of Fixed Points, Springer, Berlin, 2007.
[3] Phuengrattana, Withun, and Suthep Suantai. "On the Rate of Convergence of Mann, Ishikawa,
Noor and SP Iterations for Continuous on an Arbitrary Interval." J. Comput. Appl. Math. 235(2011),
3006-3914.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
104
ON EXISTENCE AND UNIQUINESS OF SOME CLASS NONLINEAR
EIGENVALUE PROBLEM
Yusuf ZEREN1 and Lutfi AKIN2
1Yildiz Technical University, Faculty of Science, Istanbul,Turkey
yzeren@yildiz.edu.tr
2Mardin Artuklu University, Faculty of Economics and Business Administration, Mardin, Turkey
lutfiakin@artuklu.edu.tr
Abstract: We will investigate on existence and uniquiness of some class nonlinear eigenvalue
problem.
Keywords: Variable exponent, operator theory, Lebesgue spaces
In this work, we derive a new boundedness and compactness result for the Hardy operator in variable
Lebesgue spaces (VELS) 𝐿𝑝(.)(0, 𝑙). A maximally weak condition is assumed on the exponent
function. For a study the Dirichlet problem of some class nonlinear eigenvalue problem with
nonstandard growth condition the obtained results is applied. In this connection, we mention recent
studies for the multidimensional cases with application of Ambrosetti-Rabinoviche’s Mountain pass
theorem approaches (see, e.g. in [1, 2, 3]) .
Theorem 1. Let 𝑞, 𝑝 ∶ (0, 𝑙) → (1, ∞) be measurable functions with 𝑞(𝑥) ≥ 𝑝(𝑥) on (0, 𝑙) . Assume 𝑝
be monotony increasing and the function 𝑥−
1
𝑝′(𝑥)+𝛿
is almost decreasing on (0, 𝑙).. Then operator H
boundedly acts the space 𝐿𝑝(0, 𝑙) into 𝐿𝑞(.), −
1
𝑝′ −1
𝑞(.)(0, 𝑙). Moreover, the norm of mapping depends
on 𝑝−, 𝑝+, 𝛿, 𝛽.
Theorem 2. Let 𝑞, 𝑝 ∶ (0, 𝑙) → (1, ∞) be measurable functions such that ∞ > 𝑞+ ≥ 𝑞(𝑥) ≥ 𝑝(𝑥) ≥
𝑝− > 1 for all 𝑥 ∈ (0, 𝑙). Assume that 𝑝 be monotony increasing and 𝑥−
1
𝑝′+ is almost decreasing.
Then the identity operator maps boundedly the space 𝑊𝑝(.)1. (0, 𝑙) into 𝐿
𝑞(.),−1
𝑝′ −1
𝑞(.)(0, 𝑙). Moreover,
the norm of mapping is estimated by a constant depending on 𝑝−, 𝑝+, 𝑞, 휀, 𝛽.
Notice, Theorem 2 states the inequality
‖𝑦𝑥 −
1
𝑝′ −1
𝑞(.)‖𝐿𝑞(.)(0,𝑙)
≤ ‖𝑦′‖𝐿𝑝(.)(0,𝑙) (1)
for any absolutely continues function 𝑦: (0, 𝑙) → ℝ with 𝑦(0) = 0.
References:
[1] Ambrosetti, P. Rabinowitz, Dual variational methods in critical point theory and applications, J.
Funct. Anal. 14 , 349–381, 1973.
[2] F.I. Mamedov and A. Harman On a Hardy type general weighted inequality in spaces
𝐿𝑝(.)(0, 𝑙). Integr. Equ. Oper. Th., 66(1), 565-592, 2010.
[3] V. D. Radulescu, Nonlinear elliptic equations with variable exponent: Old and new, Nonlinear
Analysis, 121, 336–369, 2015.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
105
OBTAINING THE FINITE DIFFERENCE APPROXIMATION OF TRANSMISSION
CONDITIONS OF DEFORMATION PROBLEM FOR MULTILAYERED
MATERIALS
Zahir MURADOGLU1, Vildan YAZICI1, Tatsiana URBANOVICH1,2
1Department of Mathematics, Kocaeli University, Izmit, Turkey,
zahir@kocael.edu.tr, maths.vildan@gmail.com
2Department of Higher Mathematics, Polotsk State University, Belarus
urbanovichtm@gmail.com
Abstract: In this study, we use finite element method to obtain the numerical solution of the plane
deformation problem for multilayered materials. The mathematical model of the problem is expressed
by the system of Lame equations. Some differences of the mechanical properties of the materials
composed the layers make it impossible to solve such problems with classical finite difference
methods. In this work, to ensure continuity at the common boundary between the layers, we obtain
the numerical expressions of the transmission conditions by using the finite element method. The
relation between the numerical expressions obtained by using finite element method and finite
differences method is shown.
Keywords: Finite element method, Lame equation, Laminated medium; transmission conditions.
Acknowledgement: This work is supported by the TUBITAK program 2221 - "Fellowship Program
For Visiting Scientists and Scientists on Sabbatical Leave".
References:
[1] G.M.L. Gladwell, Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff,
Alphen aan den Rijn, The Netherlands, 1980.
[2] N.J. Pindera, M.S. Lane, Frictionless contact of layered half-planes, ASME J. Appl. Mech. 60
(1993) 633–645.
[3] Z. Seyidmamedov, Finite-element analysis of frictionless contact problem for a laminated
medium, Mathematics and Computers in Simulation 58 (2002) 111–123.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
106
POSTER SESSION
SUMS OF ELEMENT ORDERS IN FINITE GROUPS
Ayşe Nur KÖKSAL1, Nil MANSUROĞLU2
1,2Department of Mathematics, Kırşehir Ahi Evran University, 40100 Kırşehir, Turkey,
aysenur4026@gmail.com
nil.mansuroglu@ahievran.edu.tr
Abstract: We investigate the sum of element orders of finite groups in literature and, our purpose is
to formulate the sum of element orders of symmetric groups in the light of works and used methods
in articles of H. Amiri, S.M. Jafarian Amiri and I.M. Isaacs with M. Tarnauceanu and D. Gregorian
Fodor.
Keywords: finite group, element order, sum of element orders.
References:
[1] H. Amiri, S.M. Jafarian Amiri, I.M. Isaacs, Sums of element orders in finite groups, Comm.
Algebra, 37, (2009), 2978-2980.
[2] M. Tarnauceanu, D. Gregorian Fodor, On the sum of element orders of finite abelian groups,
10.2478/ aicu-2013-0013.
[3] H. Amiri, S.M. Jafarian Amiri, Sum of element orders on finite groups of the same order, J.
Algebra Appl., 10 (2), (2011), 187-190.
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
107
APPROXIMATION BY GENERALIZED COMPLEX SZÁSZ-MIRAKYAN
OPERATORS IN COMPACT DISK
Döne KARAHAN1, Sevilay K. SERENBAY2, Aydın İZGİ3
1,2,3Department of Mathematics, Harran University, Osmanbey Campus, Şanlıurfa, Turkey,
dkarahan@harran.edu.tr
sevilaykirci@gmail.com
aydinizgi@yahoo.com
Abstract: In this study, the generalized complex Szász-Mirakyan operators are introduced and the
approximation properties of these operators are studied. The Voronovskaya's theorem with
quantitative estimate for these operators attached to analytic function is obtained on compact disks.
Keywords: Complex Szász-Mirakyan operators, quantitative exact approximation, Voronovskaya's
theorem
References:
[1] Lorentz, G.G: Bernstein polynomials, 2nd edn. Chelsea, New York, ISBN:0-8284-0323-6
(1986).
[2] Gal GS. Approximation by complex Bernstein and convolution type operators. World Scienti_c
Publ. Co., Singapore (2009).
[3] Serenbay, S.K, Dalmanoglu, O: Rate of convergence for generalized Szász-Mirakyan operators
in exponential weighted space. Applications and Applied Math. 12:2, 884-897 (2017).
[4] Gupta, V, Verma, K.D: Approximation by complex Favard-Szász-Mirakjan-Stancu operators in
compact disks. Mathematical Sciences. 6:25 (2012).
[5] Korovkin, P. P: On convergence of linear positive operators in the space of continuous
functions. Dokl. Akad. Nauk, 90, 961-964 (1953).
[6] Kantorovich, L. V: Sur certains developments suivant les polynomes de la forms de S.Bernstein
I, II, Dokal Akad Nauk SSSR, 595-600, 563-568, (1930).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
108
ON APPROXIMATION BY GENERALIZED BERNSTEIN-KANTOROVICH
OPERATORS OF TWOVARIABLE
Döne KARAHAN1, Aydın İZGİ2
1,2Department of Mathematics, Harran University, Osmanbey Campus, Şanlıurfa, Turkey,
dkarahan@harran.edu.tr
aydinizgi@yahoo.com
Abstract: In this study, the generalized Bernstein-Kantorovich type operators are introduced and
some approximation properties of these operators are studied in the space of continuous functions
of two variables on a compact set . The convergence rate of these operators are obtained by means
of the modulus of continuity. The Voronovskaya type theorem is given and some differential
properties of these operators are proved.
Keywords: Bernstein-Kantorovich type operator, modulus of continuity, Voronovskaya type
theorem.
References:
[1] Bernstein, S. N: Demonstration du theorem de Weierstrass fondee sur le calculu des
probabilites. Comp. Comm. Soc. Mat. Charkow Ser., 13(2), 1-2 (1912).
[2] Kantorovich, L. V: Sur certains developments suivant les polynomes de la forms de S.Bernstein
I, II, Dokal Akad Nauk SSSR, 595-600, 563-568, (1930).
[3] Korovkin, P. P: On convergence of linear positive operators in the space of continuous
functions. Dokl. Akad. Nauk, 90, 961-964 (1953).
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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NON PRESENTING PARTICIPANTS
Zhamile ASKEROVA Arzu d. OĞUZ Fatih DERİNGÖZ İsmail Onur KIYMAZ Ayşegül ÇETİNKAYA Emirhan HACIOĞLU Cem OĞUZ Sezin AYKURT SEPET Zehra GÜZEL ERGÜL Hasan ALTINBAŞ Şebnem YILDIZ Hatice ÖZKAN Sena HALICI Fatma ÇOLAK Hasan BULUT Emine ÖNAL KIR Emre TAŞ Faruk YILMAZ Farah M. MİSLAR Yasin KARAKAYA Tuba DEMİRAY Reyhan ÖZÇELİK Nil MANSUROĞLU Nagehan KILINÇ GEÇER Cenk YILDIRIM Musa DİKMEN M.Fatih KARAASLAN Gülden GÜRSOY Fatma KOÇAKER ALTUN Yılmaz ALTUN Zhor MELLAH A. Canan GÜNEŞ Merve DEMİREL Esra Nur SOYLU Guyguy Mande MABEKE Oulgiht BADR Dada LASSYED Adeeb SAEED Abduraxim ABDUGANIYEV Isaac Kwabena ADOMAKO Jonathan Osei OWUSU Abdullah ANSARI Gülistan İSKANDAROVA Kader ŞİMŞİR ACAR Caner KAZAR
İstanbul Commerce University Atılım University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Yildiz Technical University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Düzce University Fırat University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Düzce University Düzce University Kırşehir Ahi Evran University Kırşehir Ahi Evran University Yildiz Technical University Adıyaman University Yildiz Technical University Şehit Cem Özgül OO. Kırşehir Ahi Evran University Kırşehir Ahi Evran University University Mohammed First, Oujda Kırşehir Ahi Evran University Kırşehir Ahi Evran University Ege University Mathematic and Computer Shardfo-tech Company Limited Shardfo-tech Company Limited Amu İstanbul Commerce University Yildiz Technical University Yildiz Technical University
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
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INDEX
A
Aakif Fairooze TALEE .................................................. 73
Abdulmajid NUSAYR ................................................... 18
Akhilesh PRASAD ........................................................ 19
Arife Aysun KARAASLAN ......................................... 7, 20
Arzu ÖZKOÇ ÖZTÜRK .................................................. 21
Asıf YOKUS ................................................................. 22
Aydın İZGİ.................................................... 74, 108, 107
Aynur ŞAHİN .............................................................. 23
Ayşe Nur KÖKSAL ...................................................... 106
Ayşe SARIAYDIN-FİLİBELİOĞLU .................................... 24
B
Bayram ŞAHİN .............................................................. 6
Burak KURT ................................................................ 25
C
Canan AYDEMIR ......................................................... 92
Cihan UNAL ..................................................... 26, 57, 58
Cuneyt YAZICI ............................................................. 27
D
Derya KARATAŞ .......................................................... 28
Derya SEKMAN ......................................................29, 30
Dogan KAYA ............................................................... 31
Döne KARAHAN ................................................. 107, 108
Driss KARIM ............................................................... 55
Duran TURKOGLU ....................................................... 49
E
Emrah Evren KARA ................................................32, 86
Erdal ÜNLÜYOL ........................................................... 33
Erdinç DÜNDAR .................................... 34, 78, 79, 98, 63
Erhan GÜLER ............................................. 35, 36, 82, 83
Erkut ALİMERT.......................................................... 103
Esra GÜLLE ............................................................37, 99
F
Faik GÜRSOY ............................................ 6, 7, 38, 69, 72
Fatih NURAY ........................................................... 6, 34
Ferhat SAH ............................................................39, 40
Fernane KHAIREDDINE ................................................ 41
Fuat USTA .................................................................. 42
Funda TAŞDEMİR ........................................................ 43
G
G. Canan HAZAR GÜLEÇ .............................................. 44
G. Zamani ESKANDANI ................................................ 45
Gonca DURMAZ .......................................................... 46
Gulistan ISKANDAROVA .............................................. 31
H
Haci Mehmet BASKONUS ...................................... 47, 48
Hakan SAHIN .............................................................. 49
Hamdullah ŞEVLİ..................................................... 6, 50
Hamid VAEZI .............................................................. 51
Handan KOSE ............................................................. 52
Harun POLAT ........................................................ 54, 88
Hasan BULUT .............................................................. 84
Hassan MOUADI ......................................................... 55
Hatice ASLAN HANÇER ................................................ 46
Havva TİLKİ ................................................................. 53
Hulya KODAL SEVİNDİR ............................................... 27
I
Ismail AYDIN .................................................... 26, 57, 58
İ
İbrahim GÖKCAN ........................................................ 56
İshak ALTUN ......................................................... 46, 49
İsmail AYDIN ............................................................... 85
İsmail TAŞTEKİN .......................................................... 43
J
Javid ALI ....................................................................... 7
Jong Kyu KIM .............................................................. 14
K
Kadri DOĞAN ........................................................ 59, 60
L
Lutfi AKIN ................................................................. 104
4th International Conference on Analysis and Its Applications, September 11-14, 2018, Kirsehir,Turkey, icaa2018.ahievran.edu.tr
111
M
M. Ali SARIGÖ2 ........................................................... 44
M. RAEISI ................................................................... 45
M. SARI ...................................................................... 68
M. Yahya ABBASI ........................................................ 73
Mehmet GÜRDAL ....................................................... 53
Merve İLKHAN ............................................................ 61
Mikail ET .................................................................... 75
Mohamad NAGHLISAR ................................................ 51
Mohammad KNEFATI .................................................. 62
Mohammad MURSALEEN ................................ 5, 6, 7, 15
Mualla Birgül HUBAN .................................................. 53
Muhammed Recai TÜRKMEN ..................... 63, 64, 65, 66
Muhammet KURULAY ............................................... 101
Murat KİRİŞCİ ............................................................. 67
Murat OLGUN ............................................................ 46
Musa DİKMEN ............................................................ 69
Muttalip ÖZAVŞAR...................................................... 70
Mücahit ÖZKAYA ........................................................ 71
Müzeyyen ERTÜRK ................................................72, 38
N
Nadire Fulda ODABAŞI ................................................ 74
Necip ŞİMŞEK ........................................................75, 76
Nejla ÖZMEN .............................................................. 77
Nil MANSUROĞLU ......................................... 28, 71, 106
Nimet P. AKIN........................................................78, 79
Nursel CETIN .............................................................. 81
O
Ozlem KIRCI ................................................................ 84
Ö
Ömer KİŞİ .................................................. 82, 83, 35, 36
ÖZER TALO ................................................................. 96
Özlem ESEN ................................................................ 97
Öznur KULAK .............................................................. 85
P
Pınar ZENGİN ALP ....................................................... 86
Q
Qamrul Hasan ANSARI ............................................ 5, 13
R
Ruken ÇELİK ............................................................... 76
S
S. Ali-TAHIR ................................................................ 68
Sabahat Ali KHAN ....................................................... 73
Serpil HALICI ............................................................... 87
Sevilay K. SERENBAY ................................................. 107
Sevim ASLAN .............................................................. 87
Sibel ÖZTÜRK.............................................................. 88
Sibel YALÇIN TOKGÖZ ..................... 89, 90, 91, 93, 94, 95
Suleyman CETINKAYA ................................................. 27
Sultan Abaci CELIK ...................................................... 92
Ş
Şahsene ALTINKAYA........................ 93, 94, 95, 89, 90, 91
Şükrü TORTOP ............................................................ 96
T
Taner BÜYÜKKÖROĞLU ............................................... 97
Tanuj KUMAR ............................................................. 19
Tatsiana URBANOVICH.............................................. 105
U
Uğur ULUSU ......................................... 34, 37, 78, 98, 99
V
Vakıf CAFER ................................................................ 97
Vatan KARAKAYA ........................ 4, 7, 20, 29, 30, 62, 102
Vildan YAZICI ............................................................ 105
W
Waleed KHEDR ......................................................... 100
Y
Yaprak DERICIOGLU .................................................. 101
Yeter ERDAŞ ............................................................... 33
Yılmaz ALTUN ............................................................. 59
Yunus ATALAN ................................................... 102, 103
Yurdal SEVER .............................................................. 96
Yusuf ZEREN ............................................................. 104
Z
Zahir MURADOGLU ................................................... 105
Zhamile ASKEROVA ..................................................... 76
Zuhair NASHED ....................................................... 6, 16
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