Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 11Citation - Scopus: 11Best 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; MatematikWe 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.Article Citation - WoS: 146Citation - Scopus: 166On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions(Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Karapınar, Erdal; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; MatematikThe aim of this article is twofold. Firstly, to study fixed points of mappings on b metric spaces satisfying a general contractive condition called Geraghty type hybrid contraction. Secondly, to apply the theoretical results to the problem of existence and uniqueness of solutions of boundary value problems with integral boundary conditions associated with a certain type of nonlinear fractional differential equations. The conditions for the existence of fixed points for Geraghty type hybrid contractions are determined and several consequences of the main results are deduced. Some examples on boundary value problems for nonlinear fractional differential equations of order 3 < alpha <= 4 are provided, where the existence and uniqueness of solutions are shown by using Geraghty type contractions.Article Ample Spectrum Contractions in Branciari Distance Spaces(Yokohama Publ, 2021) Karapinar, Erdal; Karapınar, Erdal; Lopez de Hierro, Antonio Francisco Roldan; Shahzad, Naseer; De Hierro, A.F.R.L.; MatematikVery 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.Article Citation - WoS: 35On Interpolative Boyd-Wong and Matkowski Type Contractions(inst Applied Mathematics, 2020) Karapinar, Erdal; Karapınar, Erdal; Aydi, Hassen; Mitrovic, Zoran D.; MatematikBy using an interpolation approach, we recognize Boyd-Wong and Matkowski type contractions and we prove the related fixed point theorems in the class of metric spaces. The obtained results are supported by some examples. We also give the partial metric case according to our results.Article Citation - WoS: 22Citation - Scopus: 28Non-Instantaneous Impulsive Fractional Integro-Differential Equations With State-Dependent Delay Br(Univ Maragheh, 2022) Salim, Abdelkrim; Aissani, Khalida; Benchohra, Mouffak; Karapinar, Erdal; Benkhettou, NadiaThis paper deals with the existence and uniqueness of the mild solution of the fractional integro-differential equations with non-instantaneous impulses and state-dependent delay. Our arguments are based on the fixed point theory. Finally, an example to confirm of the results is provided.Article Citation - WoS: 6Citation - Scopus: 9Neutral Functional Sequential Differential Equations With Caputo Fractional Derivative on Time Scales(Springernature, 2022) Lazreg, Jamal Eddine; Benkhettou, Nadia; Benchohra, Mouffak; Karapinar, ErdalIn this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray-Schauder type and Krasnoselskii fixed point theorem. As applications, two examples are included to show the applicability of our results.Article Citation - WoS: 12Citation - Scopus: 16Super Metric Spaces(Univ Nis, Fac Sci Math, 2022) Karapinar, Erdal; Khojasteh, FarshidThe aim of this paper is to propose a new generalization of metric space which may open a new framework. As an application, we consider the analog of Banach contraction mapping principle that works properly.Article Citation - WoS: 1Citation - Scopus: 4Fixed Point Theorems for Mappings With a Contractive Iterate at a Point in Modular Metric Spaces(House Book Science-casa Cartii Stiinta, 2022) Karapinar, Erdal; Aksoy, Umit; Fulga, Andreea; Erhan, Inci M.In this manuscript, we introduce two new types of contraction, namely, w-contraction and strong Sehgal w-contraction, in the framework of modular metric spaces. We indicate that under certain assumptions, such mappings possess a unique fixed point. For the sake of completeness, we consider examples and an application to matrix equations.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.Article Citation - WoS: 14Citation - Scopus: 17Interpolative Meir-Keeler Mappings in Modular Metric Spaces(Mdpi, 2022) Fulga, Andreea; Yesilkaya, Seher Sultan; Karapinar, ErdalModular metric space is one of the most interesting spaces in the framework of the metric fixed point theory. The main goal of the paper is to provide some certain fixed point results in the context of modular metric spaces and non-Archimedean modular metric spaces. In particular, we examine the existence of interpolative Meir-Keeler contraction types via admissible mappings for fixed point theory. Our results bring together several results available in the current corresponding literature.