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Article Citation - WoS: 5Citation - Scopus: 6Mild 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.Article Citation - WoS: 41Citation - Scopus: 52Discussion on Generalized-(αψ, Βφ)-Contractive Mappings Via Generalized Altering Distance Function and Related Fixed Point Theorems(Hindawi Ltd, 2014) Berzig, Maher; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-FranciscoWe extend the notion of (alpha psi, beta phi)-contractive mapping, a very recent concept by Berzig and Karapinar. This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. Thus, using this kind of contractive mappings, we show some related fixed point theorems that improve some well known recent results and can be applied in a variety of contexts.Article Citation - WoS: 2Citation - Scopus: 19Periodic Points of Weaker Meir-Keeler Contractive Mappings on Generalized Quasimetric Spaces(Hindawi Publishing Corporation, 2014) Lin, Ing-Jer; Chen, Chi-Ming; Karapinar, ErdalBy using the weaker Meir-Keeler function phi and the triangular alpha-admissible mapping alpha, we introduce the notion of (alpha - phi)-weaker Meir-Keeler contractive mappings and prove a theorem which assures the existence of a periodic point for these mappings on generalized quasimetric spaces.Article Citation - WoS: 59Citation - Scopus: 68Generalized (c)-conditions and Related Fixed Point Theorems(Pergamon-elsevier Science Ltd, 2011) Karapinar, Erdal; Tas, Kenan; Karapnar, ErdalIn this manuscript, the notion of C-condition [K. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] is generalized. Some new fixed point theorems are obtained. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 8Citation - Scopus: 8Berinde Mappings in Ordered Metric Spaces(Springer-verlag Italia Srl, 2015) Karapinar, Erdal; Sadarangani, KishinRecently, Samet and Vetro proved a fixed point theorem for mappings satisfying a general contractive condition of integral type in orbitally complete metric spaces (Samet and Vetro, Chaos Solitons Fractals 44:1075-1079, 2011). Our aim in this paper is to present a version of the results obtained in the above mentioned paper in the context of ordered metric spaces. Some examples are presented to distinguish our results from the existing ones.Article Citation - WoS: 23Citation - Scopus: 31A Discussion on "α-Ψ Contraction Type Mappings "(Univ Nis, Fac Sci Math, 2014) Karapinar, ErdalIn this paper we discuss the subadditivity property of some auxiliary functions which have been used to generalize the contractive conditions on maps. Our results show that this property is not required in many cases and therefore, can be removed. We emphasize that in several papers (see e.g.[1]-[11]) dealing with such contraction mappings, the hypotheses of the main theorems can be restated in the light of our results.Article Citation - WoS: 27Citation - Scopus: 29ON α-ψ-GERAGHTY CONTRACTION TYPE MAPPINGS ON QUASI-BRANCIARI METRIC SPACES(Yokohama Publ, 2016) Karapinar, Erdal; Pitea, ArianaIn this paper, we state and prove results regarding alpha-psi-Geraghty contractive mappings in the setting of quasi-Branciari metric spaces. We provide existence and uniqueness results for periodic and fixed points of such mappings.Article Citation - WoS: 3Citation - Scopus: 4A New Class of Generalized Contraction Using p-functions in Ordered Metric Spaces(Sciendo, 2015) Amor, Sana Hadj; Karapinar, Erdal; Kumam, PoomIn this paper, we introduced and studied a new class of mappings in ordered metric spaces that is inspired from the concept of a P-function introduced in Chaipunya et. al. [10]. With our new class, we furnish fixed point theorems for continuous, noncontinuous, monotonic, and nonmonotonic mappings in various kinds of the ordering structures.Article Citation - WoS: 5On Some Fixed Point Results in Extended Strong b-spaces(int Center Scientific Research & Studies, 2018) Alqahtani, Badr; Karapinar, Erdal; Khojasteh, FarshidIn this paper, we propose a notion of a strong extended b-metric space and investigate the existence and uniqueness of a fixed point of certain operators.Article Citation - WoS: 12Citation - Scopus: 13Some Fixed Point Results on Interpolative Metric Spaces(Pergamon-elsevier Science Ltd, 2025) Karapinar, Erdal; Agarwal, Ravi P.This paper aims to introduce some basic fixed point theorems on interpolative metric space that is a natural extension of standard metric space.
