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Article Citation - WoS: 57Citation - Scopus: 71Fixed Point Theorems for Α-Geraghty Contraction Type Maps in Metric Spaces(Springer int Publ Ag, 2013) Cho, Seong-Hoon; Bae, Jong-Sook; Karapinar, ErdalIn this paper, we introduce a notion of alpha-Geraghty contraction type maps in the setting of a metric space. We also establish some fixed point theorems for such maps and give an example to illustrate our results. Finally, we discuss the application of our main results in the research fields of ordinary differential equations.Article Citation - WoS: 93Solution of Fractional Differential Equations Via Coupled Fixed Point(Texas State Univ, 2015) Afshari, Hojjat; Kalantari, Sabileh; Karapinar, ErdalIn this article, we investigate the existence and uniqueness of a solution for the fractional differential equation by introducing some new coupled fixed point theorems for the class of mixed monotone operators with perturbations in the context of partially ordered complete metric space.Article Citation - WoS: 15Citation - Scopus: 21A Short Note on c*-valued Contraction Mappings(Springeropen, 2016) Alsulami, Hamed H.; Agarwal, Ravi P.; Karapinar, Erdal; Khojasteh, FarshidIn this short note we point out that the recently announced notion, the C*-valued metric, does not bring about a real extension in metric fixed point theory. Besides, fixed point results in the C*-valued metric can be derived from the desired Banach mapping principle and its famous consecutive theorems.Article Citation - WoS: 17Citation - Scopus: 20Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces(Hindawi Ltd, 2015) De la Sen, Manuel; Karapinar, ErdalThis paper investigates properties of convergence of distances of p-cyclic contractions on the union of the p subsets of an abstract set X defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points of p-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of the p-composite mappings restricted to each of the p subsets in the cyclic disposal are also investigated and some illustrative examples are given.Article Citation - WoS: 25Citation - Scopus: 31Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems(Springer int Publ Ag, 2013) Kumam, Poom; Aydi, Hassen; Karapinar, Erdal; Sintunavarat, WutipholIn this paper, we introduce a multi-valued cyclic generalized contraction by extending the Mizoguchi and Takahashi's contraction for non-self mappings. We also establish a best proximity point for such type contraction mappings in the context of metric spaces. Later, we characterize this result to investigate the existence of best proximity point theorems in uniformly convex Banach spaces. We state some illustrative examples to support our main theorems. Our results extend, improve and enrich some celebrated results in the literature, such as Nadler's fixed point theorem, Mizoguchi and Takahashi's fixed point theorem.Article Citation - WoS: 4Citation - Scopus: 3On Orlicz-Power Series Spaces(Springer Basel Ag, 2010) Karapinar, Erdal; Zakharyuta, VyacheslavIn this manuscript, we investigate the isomorphisms of Orlicz-Kothe sequence spaces and quasidiagonal isomorphisms of Cartesian products of Orlicz-power series spaces.Article Citation - WoS: 21Citation - Scopus: 20Coupled Coincidence Point Theorem in Partially Ordered Metric Spaces Via Implicit Relation(Hindawi Ltd, 2012) Nguyen Manh Hung; Karapinar, Erdal; Nguyen Van LuongWe prove a coupled coincidence point theorem for mappings F : X x X -> X and g : X -> X, where F has the mixed g-monotone property, in partially ordered metric spaces via implicit relations. Our result extends and improves several results in the literature. Examples are also given to illustrate our work.Article Citation - WoS: 29Citation - Scopus: 50Non-Unique Fixed Point Results in Extended b-metric Space(Mdpi, 2018) Alqahtani, Badr; Fulga, Andreea; Karapinar, ErdalIn this paper, we investigate the existence of fixed points that are not necessarily unique in the setting of extended b-metric space. We state some examples to illustrate our results.Article Citation - WoS: 41Citation - Scopus: 44Some New Fixed Point Theorems in Fuzzy Metric Spaces(Ios Press, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Manro, SaurabhThe aim of this paper is to introduce a new class of contractive mappings such as fuzzy alpha-psi-contractive mappings and to present some fixed point theorems for such mappings in complete fuzzy metric space in the sense of Kramosil and Michalek. The results presented in this paper substantially generalize and extend several comparable results in the existing literature. Also, some examples are given to support the usability of our results.Article Citation - WoS: 35Citation - Scopus: 39Metric-Like Spaces To Prove Existence of Solution for Nonlinear Quadratic Integral Equation and Numerical Method To Solve It(Elsevier Science Bv, 2018) Hazarika, Bipan; Karapinar, Erdal; Arab, Reza; Rabbani, MohsenThe purpose of this paper is to obtain some common fixed point results for two mappings satisfying various contractive conditions in metric-like spaces. These results extend some previous results in the literature, since the condition under which the operator admits common fixed points is more general than the others in literature. Therefore, several well known results are generalized. As an application we use these results to existence of solution for nonlinear quadratic integral equation. To credibility, we apply modified homotopy and Adomian decomposition method to find solution of the above problem with high accuracy. (C) 2017 Elsevier B.V. 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