Browsing by Author "Karapinar, Erdal"

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A common fixed point theorem of a Greguš type on convex cone metric spaces
(2011) Abdeljawad, Thabet; Karapinar, Erdal; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The result of Ćirić [1] on a common fixed point theorem of Greguš type on metric spaces is extended to the class of cone metric spaces. Namely, a common fixed point theorem is proved in s-convex cone metric spaces under the normality of the cone and another common fixed point theorem is proved in convex cone metric spaces under the assumption that the cone is strongly minihedral.
Citation - WoS: 1
Citation - Scopus: 2
Abstract Random Differential Equations With State-Dependent Delay Using Measures of Noncompactness
(Vilnius Univ, inst Mathematics & informatics, 2024) Heris, Amel; Bouteffal, Zohra; Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, Erdal; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper is devoted to the existence of random mild solutions for a general class of second-order abstract random differential equations with state-dependent delay. The technique used is a generalization of the classical Darbo fixed point theorem for Frechet spaces associated with the concept of measures of noncompactness. An application related to partial random differential equations with state-dependent delay is presented.
Citation - WoS: 5
Advances on Fixed Point Results on Partial Metric Spaces
(Springer international Publishing Ag, 2019) Rakocevic, Vladimir; Karapinar, Erdal; Tas, Kenan; 1918; 4971; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 14
Citation - Scopus: 9
Advances on the Fixed Point Results Via Simulation Function Involving Rational Terms
(Springer, 2021) Chen, Chi-Ming; Alghamdi, Maryam A.; Fulga, Andreea; Karapinar, Erdal; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we propose two new contractions via simulation function that involves rational expression in the setting of partial b-metric space. The obtained results not only extend, but also generalize and unify the existing results in two senses: in the sense of contraction terms and in the sense of the abstract setting. We present an example to indicate the validity of the main theorem.
Ample Spectrum Contractions in Branciari Distance Spaces
(Yokohama Publ, 2021) Karapinar, Erdal; Karapınar, Erdal; Lopez de Hierro, Antonio Francisco Roldan; Shahzad, Naseer; 19184; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Very recently, the notion of ample spectrum contraction has been introduced in order to unify, under the same axioms, a large number of contractive mappings that have had great success in the field of Fixed Point Theory in recent years and that have been used in a wide variety of applications in Nonlinear Analysis (Meir-Keeler contractions, Geragthy contractions, contractions under simulation functions, contractions under R-functions, etc.) However, the subtle conditions that define ample spectrum contractions cannot be extended as they are to new kinds of abstract metric spaces because they involve key properties that are only fulfilled in metric spaces. In this paper, based on a very recent work in which the authors unravel the essential properties of the topology in Branciari spaces, we investigate the reasons why the proposed axiomatic fails in Branciari spaces and we illustrate how to overcome such drawbacks. As a consequence, we characterize the notion of ample spectrum contraction in the setting of Branciari distance spaces and we also investigate the existence and uniqueness of fixed points for such family of contractions in the context of complete Branciari distance spaces.
Citation - WoS: 103
Citation - Scopus: 105
Applying New Fixed Point Theorems on Fractional and Ordinary Differential Equations
(Springer, 2019) Karapinar, Erdal; Abdeljawad, Thabet; Jarad, Fahd; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we consider a fixed point theorem that extends and unifies several existing results in the literature. We apply the proven fixed point results on the existence of solution of ordinary boundary value problems and fractional boundary value problems with integral type boundary conditions in the frame of some Caputo type fractional operators.
Citation - WoS: 12
Citation - Scopus: 9
Best Proximity Point Results for Contractive and Cyclic Contractive Type Mappings
(Taylor & Francis inc, 2021) Karapinar, Erdal; Kanta Dey, Lakshmi; Hiranmoy, Garai; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The essential importance of the best proximity point theory is that "best proximity point theory" appears in the coincidence of "metric fixed point theory" and "optimization theory." So finding best proximity points of mappings satisfying different type of contractive conditions in different structures is one of the fascinating research topics. For this, in this article, we first introduce a new type of proximal property of a pair of subsets of a metric space, which we designate as proximal weakly compact pair. After this, we come up with some new type of proximal contractive and proximal cyclic contractive mappings. Then we investigate the existence of best proximity point(s) in these newly originated mappings in the setting of proximal weakly compact pair of subsets in a metric space.
Citation - WoS: 19
Citation - Scopus: 18
Best Proximity Point Theorems for Kt-Types Cyclic Orbital Contraction Mappings
(House Book Science-casa Cartii Stiinta, 2012) Karapınar, Erdal; Karapinar, Erdal; Petrusel, Gabriela; Taş, Kenan; Tas, Kenan; 19184; 4971; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this manuscript, three new KT-types cyclic orbital contractions are defined and some related best proximity point theorems are given. Also, the notion of KT-type cyclic orbital Meir-Keeler contraction is defined and some fixed point theorems for this class of mappings are proved. The results of this manuscript generalize some theorems, on the same subject, of several authors, such as Kirk-Srinavasan-Veeramani, Eldered-Veeramani and Karpagam-Agrawal.
Citation - WoS: 11
Citation - Scopus: 11
Best Proximity Results on Condensing Operators Via Measure of Noncompactness With Application To Integral Equations
(Chiang Mai Univ, Fac Science, 2020) Gabeleh, Moosa; Karapınar, Erdal; Asadi, Mehdi; Karapinar, Erdal; 19184; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We prove the best proximity point results for condensing operators on C-class of functions, by using a concept of measure of noncompactness. The results are applied to show the existence of a solution for certain integral equations. We express also an illsutrative examples to indicate the validity of the observed results.
Citation - WoS: 8
Citation - Scopus: 7
A Brief Overview and Survey of the Scientific Work by Feng Qi
(Mdpi, 2022) Agarwal, Ravi Prakash; Karapinar, Erdal; Kostic, Marko; Cao, Jian; Du, Wei-Shih; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the paper, the authors present a brief overview and survey of the scientific work by Chinese mathematician Feng Qi and his coauthors.
Citation - WoS: 12
Citation - Scopus: 23
Characterizations of Quasi-Metric and G-Metric Completeness Involving W-Distances and Fixed Points
(de Gruyter Poland Sp Z O O, 2022) Romaguera, Salvador; Tirado, Pedro; Karapinar, Erdal; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Involving w-distances we prove a fixed point theorem of Caristi-type in the realm of (non -necessarily T-1) quasi-metric spaces. With the help of this result, a characterization of quasi-metric completeness is obtained. Our approach allows us to retrieve several key examples occurring in various fields of mathematics and computer science and that are modeled as non-T-1 quasi-metric spaces. As an application, we deduce a characterization of complete G-metric spaces in terms of a weak version of Caristi's theorem that involves a G-metric version of w-distances.
Citation - WoS: 5
Citation - Scopus: 6
Coincidence Point Theorem on Hilbert Spaces Via Weak Ekeland Variational Principle and Application To Boundary Value Problem
(Chiang Mai Univ, Fac Science, 2021) Asadi, Mehdi; Karapınar, Erdal; Karapinar, Erdal; 19184; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we give a new coincidence point theorem for two operators on Hilbert spaces for certain operators by using the weak Ekeland variational principle. Our paper extends and improves the results on the topic in the literature. We consider a boundary value problem as an application of our results.
Citation - WoS: 8
Citation - Scopus: 11
Contraction in Rational Forms in the Framework of Super Metric Spaces
(Mdpi, 2022) Karapinar, Erdal; Fulga, Andreea; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we investigate contractions in a rational form in the context of the supermetric space, which is a very interesting generalization of the metric space. We consider an illustrative example to support this new result on supermetric space.
Citation - WoS: 28
Citation - Scopus: 43
Controllability of Second Order Functional Random Differential Equations With Delay
(Mdpi, 2022) Benchohra, Mouffak; Bouazzaoui, Fatima; Karapinar, Erdal; Salim, Abdelkrim; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we study some existence and controllability results for two classes of second order functional differential equations with delay and random effects. To begin, we employ a random fixed point theorem with a stochastic domain to demonstrate the existence of mild random solutions. Next, we prove that our problems are controllable. Finally, an example is given to validate the theory part.
Citation - WoS: 43
Citation - Scopus: 34
Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces
(Hindawi Ltd, 2012) Karapinar, Erdal; Abdeljawad, Thabet; Aydi, Hassen; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappings F : X x X -> X and g : X -> X on a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012) have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012)
Citation - WoS: 20
Citation - Scopus: 24
A Discussion on a Generalized Geraghty Multi-Valued Mappings and Applications
(Springer, 2020) Atapour, Maryam; Karapinar, Erdal; Afshari, Hojjat; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This research intends to investigate the existence results for both coincidence points and common fixed point of generalized Geraghty multi-valued mappings endowed with a directed graph. The proven results are supported by an example. We also consider fractional integral equations as an application.
Citation - WoS: 6
Citation - Scopus: 7
A Discussion on a Pata Type Contraction Via Iterate at a Point
(Univ Nis, Fac Sci Math, 2020) Fulga, Andreea; Rakocevic, Vladimir; Karapinar, Erdal; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we introduce the notion of Pata type contraction at a point in the context of a complete metric space. We observe that such contractions possesses unique fixed point without continuity assumption on the given mapping. Thus, is extended the original results of Pata. We also provide an example to illustrate its validity.
Citation - WoS: 9
Citation - Scopus: 11
A Discussion on P-Geraghty Contraction on Mw-Quasi Spaces
(Mdpi, 2020) Fulga, Andreea; Karapinar, Erdal; Tirado, Pedro; Alegre, Carmen; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper we consider a kind of Geraghty contractions by using mw-distances in the setting of complete quasi-metric spaces. We provide fixed point theorems for this type of mappings and illustrate with some examples the results obtained.
Citation - WoS: 7
Citation - Scopus: 10
A Discussion on Random Meir-Keeler Contractions
(Mdpi, 2020) Karapinar, Erdal; Chen, Chi-Ming; Li, Cheng-Yen; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The aim of this paper is to enrich random fixed point theory, which is one of the cornerstones of probabilistic functional analysis. In this paper, we introduce the notions of random, comparable MT-gamma contraction and random, comparable Meir-Keeler contraction in the framework of complete random metric spaces. We investigate the existence of a random fixed point for these contractions. We express illustrative examples to support the presented results.
Citation - WoS: 2
Citation - Scopus: 2
A Discussion on the Coincidence Quasi-Best Proximity Points
(Univ Nis, Fac Sci Math, 2021) Abkar, Ali; Karapinar, Erdal; Fouladi, Farhad; 19184; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we first introduce a new class of the pointwise cyclic-noncyclic proximal contraction pairs. Then we consider the coincidence quasi-best proximity point problem for this class. Finally, we study the coincidence quasi-best proximity points of weak cyclic-noncyclic Kannan contraction pairs. We consider an example to indicate the validity of the main result.