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Article Citation - WoS: 18Citation - Scopus: 19A Generalization of Ciric Quasicontractions(Hindawi Publishing Corporation, 2012) Karapinar, Erdal; Kieu Phuong Chi; Tran Duc ThanhWe proved a fixed point theorem for a class of maps that satisfy Ciric's contractive condition dependent on another function. We presented an example to show that our result is a real generalization.Article Citation - WoS: 25Citation - Scopus: 32Fixed Point Theorems in Complete Modular Metric Spaces and an Application To Anti-Periodic Boundary Value Problems(Univ Nis, Fac Sci Math, 2017) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.In this paper existence and uniqueness of fixed points for a general class of contractive and nonexpansive mappings on modular metric spaces is discussed. As an application of the theoretical results, the existence of a solution of anti-periodic boundary value problems for nonlinear first order differential equations of Caratheodory's type is considered in the framework of modular metric spaces.Article Citation - WoS: 6Citation - Scopus: 8Discussion on α-strictly Contractive Nonself Multivalued Maps(Springer Singapore Pte Ltd, 2016) Ali, Muhammad Usman; Kamran, Tayyab; Karapinar, ErdalIn this paper, we introduce the notions of alpha-contractive condition and strict alpha-admissibility for nonself multivalued mappings. By using these notions, we prove fixed point theorems for nonself multivalued mappings. We also construct an example to support our result.Article Citation - WoS: 6Citation - Scopus: 6Some Extensions of Fixed Point Results Over Quasi-js-spaces(Hindawi Ltd, 2016) Noorwali, Maha; Alsulami, Hamed H.; Karapinar, ErdalWe introduce the notion of quasi-JS-metric space. After defining the basic topological properties of quasi-JS-metric space, we investigate fixed point of certain mapping in the frame of complete quasi-JS-metric space. Our results unify and cover several existing fixed point theorems in distinct structures (such as standard quasi-metric spaces, quasi-b-metric spaces, dislocated quasi-metric spaces, and quasi-modular spaces) in the literature.Article Citation - WoS: 6Citation - Scopus: 5A Note on 'coupled Fixed Point Theorems for Mixed g-monotone Mappings in Partially Ordered Metric Spaces'(Springer international Publishing Ag, 2014) Bilgili, Nurcan; Erhan, Inci M.; Karapinar, Erdal; Turkoglu, DuranRecently, some (common) coupled fixed theorems in various abstract spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we noticed that most of such (common) coupled fixed theorems are either weaker or equivalent to existing fixed point results in the literature. In particular, we prove that the very recent paper of Turkoglu and Sangurlu 'Coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces [Fixed Point Theory and Applications 2013, 2013:348]' can be considered as a consequence of the existing fixed point theorems on the topic in the literature. Furthermore, we give an example to illustrate that the main results of Turkoglu and Sangurlu (Fixed Point Theory Appl. 2013:348, 2013) has limited applicability compared to the mentioned existing fixed point result.Article Citation - WoS: 1Citation - Scopus: 1Several Outcomes of Fixed-Point Theory in Interpolative Metric Spaces(Univ Politecnica Valencia, Editorial UPV, 2025) Karapinar, Erdal; Kadioglu, Kaan; Turkmenel, Merve Gulcin; Aksoy, UmitThis paper aims to generalize and improve the recent fixed-point theorems in the setting of interpolative metric spaces. More precisely, we investigate the existence and uniqueness of the fixed-point for certain operators of the Ciric-Reich-Rus-type, via admissible mapping in the context of interpolative metric spaces.Article Citation - WoS: 70Citation - Scopus: 68Best Proximity Points of Cyclic Mappings(Pergamon-elsevier Science Ltd, 2012) Karapinar, ErdalIn this this manuscript, we proved that the existence of best proximity points for the cyclic operators T defined on a union of subsets A, B of a uniformly convex Banach space X with T (A) subset of B, T(B) subset of A and satisfying the condition parallel to Tx - Yy parallel to <= alpha/3[parallel to x-y parallel to + parallel to Tx - x parallel to + parallel to Ty - y parallel to] + (1 - alpha)diam(A, B) for alpha is an element of (0, 1) and for all x is an element of A, for all y is an element of B, where diam(A, B) = inf{parallel to x - y parallel to : x is an element of A, y is an element of B}. (C) 2012 Elsevier Ltd. All rights reserved.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: 48Citation - Scopus: 45Fixed Point Results for gm< Contractive and g-(α, Ψ)-Meir Contractive Mappings(Springer international Publishing Ag, 2013) Hussain, Nawab; Karapinar, Erdal; Salimi, Peyman; Vetro, PasqualeIn this paper, first we introduce the notion of a G(m)-Meir-Keeler contractive mapping and establish some fixed point theorems for the G(m)-Meir-Keeler contractive mapping in the setting of G-metric spaces. Further, we introduce the notion of a G(c)(m)-Meir-Keeler contractive mapping in the setting of G-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a G-(alpha, psi)-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces.Article Citation - WoS: 6Citation - Scopus: 9On Interpolative Metric Spaces(Univ Nis, Fac Sci Math, 2024) Karapinar, ErdalThe purpose of this article is to expand the "open discussion" on the definition and necessity of the interpolation metric space and keep it on the agenda of researchers in nonlinear functional analysis. The secondary aim of this article is to indicate that the outcomes of this "open discussion" have the potential to stop the recent recession in the metric fixed point theory.
