Karapınar, Erdal
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Karapınar, E.
Karapinar, E.
Karapinar, Erdal
Erdal Karapinar
Karapinar, E.
Karapinar, Erdal
Erdal Karapinar
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02.02. Matematik
Matematik
02. Fen-Edebiyat Fakültesi
01. Çankaya Üniversitesi
Matematik
02. Fen-Edebiyat Fakültesi
01. Çankaya Üniversitesi
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179 results
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Now showing 1 - 10 of 179
Article Citation - WoS: 1Citation - Scopus: 1Fixed Point Results for Frum-Ketkov Type Contractions in B-Metric Spaces(Mdpi, 2021) Karapinar, Erdal; Petrusel, Gabriela; Chifu, CristianThe purpose of this paper is to present some fixed point results for Frum-Ketkov type operators in complete b-metric spaces.Article Citation - WoS: 23Citation - Scopus: 26On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order(Wiley, 2023) Benkerrouche, Amar; Souid, Mohammed Said; Karapinar, Erdal; Hakem, AliIn this manuscript, we examine both the existence, uniqueness, and the stability of solutions to the boundary value problem (BVP) of Hadamard fractional differential equations of variable order by converting it into an equivalent standard Hadamard (BVP) of the fractional constant order with the help of the generalized intervals and the piecewise constant functions. All results in this study are established using Krasnoselskii fixed-point theorem and the Banach contraction principle. Further, the Ulam-Hyers stability of the given problem is examined, and finally, we construct an example to illustrate the validity of the observed results.Book Part Citation - Scopus: 15Fixed Point Theory in Generalized Metric Spaces(Springer Nature, 2022) Karapınar, E.; Agarwal, R.P.Article Citation - WoS: 10Citation - Scopus: 11On Interpolative Hardy-Rogers Type Multivalued Contractions Via a Simulation Function(Univ Nis, Fac Sci Math, 2022) Ali, Ahsan; Hussain, Azhar; Aydi, Hassen; Karapinar, ErdalIn this paper, the notion of multivalued interpolative Hardy-Rogers-contractions using generalized simulation functions is introduced. We establish some related fixed point results and we provide some examples. We also prove data dependence of the fixed point sets. Moreover, we present strict fixed point set, well-posedness and homotopy results.Article Citation - WoS: 48Citation - Scopus: 62Solutions of Boundary Value Problems on Extended-Branciari B-Distance(Springer, 2020) Panda, Sumati Kumari; Mlaiki, Nabil; Abdeljawad, Thabet; Karapinar, ErdalIn this paper, we consider a new distance structure, extended Branciari b-distance, to combine and unify several distance notions and obtain fixed point results that cover several existing ones in the corresponding literature. As an application of our obtained result, we present a solution for a fourth-order differential equation boundary value problem.Book Part Citation - Scopus: 7Fractional Differential Equations With Instantaneous Impulses(Springer Nature, 2023) Karapınar, E.; Lazreg, J.E.; Salim, A.; Benchohra, M.The aim of this chapter is to prove some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer-type fractional derivative. We base our arguments on some relevant fixed point theorems combined with the technique of measure of noncompactness. Examples are included to show the applicability of our results for each section. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.Book Fixed Point Theory in Generalized Metric Spaces(2022) Karapınar, Erdal; Agarwal, Ravi P.This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.Article Citation - WoS: 12Citation - Scopus: 9Best Proximity Point Results for Contractive and Cyclic Contractive Type Mappings(Taylor & Francis inc, 2021) Karapinar, Erdal; Kanta Dey, Lakshmi; Hiranmoy, GaraiThe 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.Article Citation - WoS: 3Citation - Scopus: 3Quadruple Fixed Point Theorems for Nonlinear Contractions on Partial Metric Spaces(Univ Politecnica Valencia, Editorial Upv, 2014) Karapinar, Erdal; Tas, KenanThe notion of coupled fixed point was introduced by Guo and Laksmikantham [12]. Later Gnana Bhaskar and Lakshmikantham in [11] investigated the coupled fixed points in the setting of partially ordered set by defining the notion of mixed monotone property. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut [7]. Following this trend, Karapmar[19] defined the quadruple fixed point. In this manuscript, quadruple fixed point is discussed and some new fixed point theorems are obtained on partial metric spaces.Article Citation - WoS: 9Citation - Scopus: 13Extended Proinov X-Contractions in Metric Spaces and Fuzzy Metric Spaces Satisfying the Property Nc by Avoiding the Monotone Condition(Springer-verlag Italia Srl, 2022) Martinez-Moreno, Juan; Shahzad, Naseer; Roldan Lopez de Hierro, Antonio Francisco; Karapinar, ErdalIn recent years, Fixed Point Theory has achieved great importance within Nonlinear Analysis especially due to its interesting applications in real-world contexts. Its methodology is based on the comparison between the distances between two points and their respective images through a nonlinear operator. This comparison is made through contractive conditions involving auxiliary functions whose role is increasingly decisive, and which are acquiring a prominent role in Functional Analysis. Very recently, Proinov introduced new fixed point results that have very much attracted the researchers' attention especially due to the extraordinarily weak conditions on the auxiliary functions considered. However, one of them, the nondecreasing character of the main function, has been used for many years without the chance of being replaced by another alternative property. In this way, several researchers have recently raised this question as an open problem in this field of study. In order to face this open problem, in this work we introduce a novel class of auxiliary functions that serve to define contractions, both in metric spaces and in fuzzy metric spaces, which, in addition to generalizing to Proinov contractions, avoid the nondecreasing character of themain auxiliary function. Furthermore, we present these new results in the setting of fuzzy metric spaces that satisfy the conditionNC, which open new possibilities in the metric theory compared to classic non-Archimedean fuzzy metric spaces. Finally, we include some illustrative examples to show how to apply the novel theorems to cases that are not covered by other previous results.
