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Article Citation - WoS: 9Citation - Scopus: 8Existence and Uniqueness of Best Proximity Points Under Rational Contractivity Conditions(Walter de Gruyter Gmbh, 2016) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Sadarangani, KishinThe main aim of this paper is to present some theorems in order to guarantee existence and uniqueness of best proximity points under rational contractivity conditions using very general test functions. To illustrate the variety of possible test functions, we include some examples of pairs of functions which are included in innovative papers published in the last years. As a consequence, we prove that our results unify and extend some recent results in this field.Article Citation - WoS: 7Citation - Scopus: 9On Cyclic Generalized Weakly c-contractions on Partial Metric Spaces(Hindawi Ltd, 2013) Karapinar, Erdal; Rakocevic, VladimirWe give new results of a cyclic generalized weakly C-contraction in partial metric space. The results of this paper extend, generalize, and improve some fixed point theorems in the literature.Article Citation - WoS: 3Citation - Scopus: 7Existence of Periodic Fixed Point Theorems in the Setting of Generalized Quasi-Metric Spaces(Hindawi Publishing Corporation, 2014) Chen, Chi-Ming; Karapinar, Erdal; Rakocevic, VladimirWe introduce the notions of (alpha - phi - psi)-weaker Meir-Keeler contractive mappings and (alpha - phi)- stronger Meir-Keeler contractive mappings. We discuss the existence of periodic points in the setting of generalized quasi-metric spaces. Our results improve, extend, and generalize several results in the literature.Article Citation - WoS: 61Best Proximity Points for Generalized α-ψ-Proximal Contractive Type Mappings(Hindawi Ltd, 2013) Jleli, Mohamed; Karapinar, Erdal; Samet, BessemWe introduce a new class of non-self-contractive mappings. For such mappings, we study the existence and uniqueness of best proximity points. Several applications and interesting consequences of our obtained results are derived.Article Citation - WoS: 22Citation - Scopus: 23A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function(Hacettepe Univ, Fac Sci, 2013) Gulyaz, Selma; Karapinar, Erdal; MathematicsIn this manuscript, we discuss the existence of coupled fixed points in the context of partially ordered metric spaces through implicit relations for mappings F:X x X -> X such that F has the mixed monotone property. Our main theorem improves and extends various results in the literature. We also state an example to illustrate our work.Article Citation - WoS: 63Citation - Scopus: 75Α-Ψ Contraction Type Mappings and Some Related Fixed Point Results(Univ Nis, Fac Sci Math, 2014) Karapinar, ErdalIn this paper, we consider a generalization of alpha-psi-Geraghty contractions and investigate the existence and uniqueness of fixed point for the mapping satisfying this condition. We illustrate an example and an application to support our results. In particular, we extend, improve and generalize some earlier results in the literature on this topic.Article Citation - WoS: 35Citation - Scopus: 43A New Approach To the Solution of the Fredholm Integral Equation Via a Fixed Point on Extended b-metric Spaces(Mdpi, 2018) Karapinar, Erdal; Kumari, Panda Sumati; Lateef, DurdanaIt is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of f(x) = x. (1) The Knaster-Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach. In this paper, by obtaining the fixed point results in an extended b-metric space, we are able to consider real-life applications in a very general frame such as a simple and efficient solution for a Fredholm integral equation by using the technique of a fixed point in the consideration of a new abstract space: the extended b-metric space. Moreover, to address conceptual depth within this approach, we supply illustrative examples of usage where necessary.Article Citation - WoS: 10Citation - Scopus: 11Fixed Point Theorems Via Auxiliary Functions(Hindawi Publishing Corporation, 2012) Karapinar, Erdal; Salimi, PeymanWe prove new fixed point theorems in the framework of partially ordered metric spaces. The main result is an extension and a generalization of many existing results in the literature. An example is also considered to illustrate the main result.Article Citation - WoS: 45Citation - Scopus: 45A Note on "some Results on Multi-Valued Weakly Jungck Mappings in b-metric Space"(versita, 2013) Bota, Monica-Felicia; Karapinar, ErdalThe proofs of Theorems 2.1, 2.2 and 2.3 from [Olatinwo M.O., Some results on multi-valued weakly jungck mappings in b-metric space, Cent. Eur. J. Math., 2008, 6(4), 610-621] base on faulty evaluations. We give here correct but weaker versions of these theorems.Article Citation - WoS: 5Citation - Scopus: 5Mild Solutions for Conformable Fractional Order Functional Evolution Equations Via Meir-Keeler Type Fixed Point Theorem(Univ Nis, Fac Sci Math, 2025) Berrighi, Fatma; Medjadj, Imene; Karapinar, ErdalIn this study, we delve into the realm of mild solutions for conformable fractional order functional evolution equations, focusing on cases where the fractional order is strictly greater than 1 and less than 2 within a separable Banach space. We demonstrate the existence, uniqueness, attractivity, and controllability of these solutions under local conditions. Our approach involves leveraging a contribution of Meir-Keeler's fixed point theorem alongside the principle of measures of noncompactness. To demonstrate the practical ramifications of our theoretical finds, we provide a specific example that underscores the relevance and applications of the established results.
