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Article Citation - WoS: 13Citation - Scopus: 18A note on some coupled fixed-point theorems on G-metric spaces(Springeropen, 2012) Ding, Hui-Sheng; Karapinar, ErdalThe purpose of this paper is to extend some recent coupled fixed-point theorems in the context of G-metric space by essentially different and more natural way. We state some examples to illustrate our results.Article Citation - WoS: 57Citation - Scopus: 74Further Fixed Point Results on g-metric Spaces(Springer int Publ Ag, 2013) Karapinar, Erdal; Agarwal, Ravi P.Very recently, Samet et al. (Int. J. Anal. 2013: 917158, 2013) and Jleli-Samet (Fixed Point Theory Appl. 2012: 210, 2012) noticed that some fixed point theorems in the context of a G-metric space can be deduced by some well-known results in the literature in the setting of a usual (quasi) metric space. In this paper, we note that the approach of Samet et al. (Int. J. Anal. 2013: 917158, 2013) and Jleli-Samet (Fixed Point Theory Appl. 2012: 210, 2012) is inapplicable unless the contraction condition in the statement of the theorem can be reduced into two variables. For this purpose, we modify some existing results to suggest new fixed point theorems that fit with the nature of a G-metric space. The expressions in our result, the contraction condition, cannot be expressed in two variables, therefore the techniques used in (Int. J. Anal. 2013: 917158, 2013; Fixed Point Theory Appl. 2012: 210, 2012) are not applicable.Article Citation - WoS: 5Citation - Scopus: 5A Solution for the Non-Cooperative Equilibrium Problem of Two Person Via Fixed Point Theory(Springeropen, 2015) Tran Duc Thanh; Hobiny, Aatef; Karapinar, ErdalIn this paper, we investigate the non-cooperative equilibrium problem of two person games in the setting of game theory and propose a solution via coupled fixed point results in the context of partial metric spaces. We also realize that our coupled fixed point results can be applied to get a solution of a class of nonlinear Fredholm type integral equations.Article Citation - WoS: 60Citation - Scopus: 72Remarks on some coupled fixed point theorems in G-metric spaces(Springer international Publishing Ag, 2013) Agarwal, Ravi P.; Karapinar, 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 - WoS: 14Citation - Scopus: 25On Coupled Fixed Point Theorems on Partially Ordered g-metric Spaces(Springeropen, 2012) Karapinar, Erdal; Kaymakcalan, Billur; Tas, KenanIn this manuscript, we extend, generalize and enrich some recent coupled fixed point theorems in the framework of partially ordered G-metric spaces in a way that is essentially more natural.Article Citation - WoS: 29Citation - Scopus: 30Coupled fixed point theorems in cone metric spaces with a c-distance and applications(Springer international Publishing Ag, 2012) Karapinar, Erdal; Kumam, Poom; Sintunavarat, WutipholIn this paper, we extend the very recent result of Sintunavarat et al. in the paper 'Coupled fixed point theorems for weak contraction mapping under F-invariant set' (Abstr. Appl. Anal. 2012:324874, 2012). In particular, we give an example of a nonlinear contraction mapping for which our result successfully detects a coupled fixed point in contrast to the result of Sintunavarat et al., which is not applied to show the existence of a coupled fixed point. As a consequence, the main results in this paper extend and unify many results in the topic of coupled fixed points including the results of Sintunavarat et al. Also, some applications of the main results are given. MSC: 54H25, 47H10.Article Citation - WoS: 13Citation - Scopus: 13Coupled Fixed Point Theorems on Partially Ordered g-metric Spaces(Springer int Publ Ag, 2012) Karapinar, Erdal; Kumam, Poom; Erhan, Inci M.The purpose of this paper is to extend some recent coupled fixed point theorems in the context of partially ordered G-metric spaces in a virtually different and more natural way.Article Citation - WoS: 25Citation - Scopus: 32Remarks on Some Recent Fixed Point Theorems(Springer international Publishing Ag, 2012) Aydi, Hassen; Karapinar, Erdal; Samet, BessemThe purpose of this article is to show that some recent fixed point theorems are particular results of previous existing theorems in the literature. Mathematics Subject Classification 2000: 54H25; 47H10.Article Citation - WoS: 10Citation - Scopus: 9A Coupled Coincidence Point Theorem in Partially Ordered Metric Spaces With an Implicit Relation(Springer international Publishing Ag, 2013) Gulyaz, Selma; Karapinar, Erdal; Yuce, Ilker SavasIn this manuscript, we discuss the existence of a coupled coincidence point for mappings and , where F has the mixed g-monotone property, in the context of partially ordered metric spaces with an implicit relation. Our main theorem improves and extends various results in the literature. We also state some examples to illustrate our work. MSC: 47H10, 54H25, 46J10, 46J15.Article Citation - WoS: 26Citation - Scopus: 19A Note on 'coupled Fixed Point Theorems for α-ψ< Mappings in Partially Ordered Metric Spaces'(Springer international Publishing Ag, 2013) Karapinar, Erdal; Agarwal, Ravi P.In this paper, we show that some examples in (Mursaleen et al. in Fixed Point Theory Appl. 2012:124, 2012) are not correct. Then, we extend, improve and generalize their results. Finally, we state some examples to illustrate our obtained results.
