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Article Citation - WoS: 11Citation - Scopus: 7Edelstein Type Fixed Point Theorems(Tusi Mathematical Research Group, 2011) Karapinar,E.; Karapınar, Erdal; Karapınar, Erdal; Mathematics; MathematicsRecently, Suzuki [Nonlinear Anal. 71 (2009), no. 11, 5313-5317.] published a paper on which Edelstein’s fixed theorem was generalized. In this manuscript, we give some theorems which are the generalization of the fixed theorem of Suzuki’s Theorems and thus Edelstein’s result [J. London Math. Soc. 37 (1962), 74-79]. © 2011, Duke University Press. All rights reserved.Article Citation - WoS: 173Fixed Point Theory for Cyclic Weak Φ-Contraction(Pergamon-elsevier Science Ltd, 2011) Karapinar, Erdal; Karapınar, Erdal; Karapınar, Erdal; Mathematics; MathematicsIn this manuscript, the notion of cyclic weak phi-contraction is considered. It is shown that a self-mapping T on a complete metric space X has a fixed point if it satisfied cyclic weak phi-contraction. (C) 2010 Elsevier Ltd. All rights reserved.Article Remarks on Some Coupled Fixed Point Theorems in G-Metric Spaces(2014) Agarwal, Ravi P.; Karapınar, ErdalIn this paper, we show that, unexpectedly, most of the coupled fixed point theorems in the context of (ordered) G-metric spaces are in fact immediate consequences of usual fixed point theorems that are either well known in the literature or can be obtained easily.Article Citation - Scopus: 1Discussion on the Equivalence of W-Distances With Ω-Distances(Yokohama Publications, 2015) Roldán-López-De-Hierro,A.-F.; Karapınar, Erdal; Karapinar,E.; Karapınar, Erdal; Mathematics; MathematicsIn this manuscript, we study some relationships between w-distances on metric spaces and Ω-distances on G*-metric spaces. Concretely we show that the class of all w-distances on metric spaces is a subclass of all Ω-distances on G*-metric spaces. Then, researchers must be careful because some recent results about w-distances (for instances, in the topic of fixed point theory) can be seen as simple consequences of their corresponding results about Ω-distances. In this sense, we show how to translate some results between different metric models. © 2015.Article Fixed Point Theory for Cyclic (j - Ψ)-Contractions(2014) Karapınar, Erdal; Sadaranganı, KishinIn this article, the concept of cyclic (j - ψ)-contraction and a fixed point theorem for this type of mappings in the context of complete metric spaces have been presented. The results of this study extend some fixed point theorems in literature.Article Citation - WoS: 43A Common Fixed Point Theorem for Cyclic Operators on Partial Metric Spaces(Univ Nis, Fac Sci Math, 2012) Karapinar, Erdal; Karapınar, Erdal; Shobkolaei, Nabi; Sedghi, Shaban; Vaezpour, S. Mansour; Karapınar, Erdal; Mathematics; MathematicsIn this paper, we prove a common fixed point theorem for two self-mappings satisfying certain conditions over the class of partial metric spaces. In particular, the main theorem of this manuscript extends some well-known fixed point theorems in the literature on this topic.Article Coincidence Point Theorems in Quasi-Metric Spaces Without Assuming the Mixed Monotone Property and Consequences in G-Metric Spaces(2014) Roldán, Antonio-francisco; Karapınar, Erdal; De La Sen, ManuelIn this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.Article Citation - WoS: 33Citation - Scopus: 34Iterative Approximation of Fixed Points for Presic Type f-contraction Operators(Univ Politehnica Bucharest, Sci Bull, 2016) Abbas, M.; Karapınar, Erdal; Berzig, M.; Nazir, T.; Karapinar, E.; Karapınar, Erdal; Mathematics; Mathematics; MathematicsWe study the convergence of the Presic type k-step iterative process for a class of operators f : X-k -> X satisfying Presic type F-contractive condition in the setting of metric spaces. As an applications of the result presented herein, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.Article Citation - WoS: 26Citation - Scopus: 26Coupled Coincidence Points for Mixed Monotone Operators in Partially Ordered Metric Spaces(Springer Heidelberg, 2012) Karapinar, Erdal; Karapınar, Erdal; Van Luong, Nguyen; Thuan, Nguyen Xuan; Karapınar, Erdal; Mathematics; MathematicsIn this paper, we give and prove some coupled coincidence point theorems for mappings F : X x X -> X and g : X -> X in partially ordered metric space X, where F has the mixed g-monotone property. Our results improve and generalize the results of Bhaskar and Lakshmikantham (Nonlinear Anal TMA 65: 1379-1393, 2006), Luong and Thuan (Bull Math Anal Appl 2(4): 16-24, 2010), Harjani et al. (Nonlinear Anal 74: 1749-1760, 2011) and Choudhury et al. (Ann Univ Ferrara 57: 1-16, 2011). We also give some examples to illustrate our results.Article Citation - WoS: 30Citation - Scopus: 37Θ-Metric Space: a Generalization(Hindawi Ltd, 2013) Khojasteh, Farshid; Karapınar, Erdal; Karapinar, Erdal; Radenovic, Stojan; Karapınar, Erdal; Mathematics; MathematicsWe introduce the notion of theta-metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a theta-metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.
