10 results
Search Results
Now showing 1 - 10 of 10
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 - Scopus: 2Remarks on Contractive Mappings Via Ω-Distance(Springeropen, 2013) Gholizadeh, Leila; Karapinar, ErdalVery recently, some authors discovered that some fixed point results in the context of a G-metric space can be derived from the fixed point results in the context of a quasi-metric space and hence the usual metric space. In this article, we investigate some fixed point results in the framework of a G-metric space via Omega-distance that cannot be obtained by the usual fixed point results in the literature. We also add an application to illustrate our results.Article Citation - WoS: 10Citation - Scopus: 15Meir-Keeler Type Contractions in Partially Ordered g-metric Spaces(Springer international Publishing Ag, 2013) Ding, Hui-Sheng; Karapinar, ErdalIn this paper, we establish several fixed point theorems for Meir-Keeler type contractions in partially ordered G-metric spaces.Article Citation - WoS: 14Citation - Scopus: 23Cyclic Contractions Via Auxiliary Functions on g-metric Spaces(Springer international Publishing Ag, 2013) Bilgili, Nurcan; Karapinar, ErdalIn this paper, we prove the existence and uniqueness of fixed points of certain cyclic mappings via auxiliary functions in the context of G-metric spaces, which were introduced by Zead and Sims. In particular, we extend, improve and generalize some earlier results in the literature on this topic.Article Citation - WoS: 8Citation - Scopus: 11g-metric Spaces in Any Number of Arguments and Related Fixed-Point Theorems(Springer international Publishing Ag, 2014) Roldan, Antonio; Karapinar, Erdal; Kumam, PoomInspired by the notion of Mustafa and Sims' G-metric space and the attention that this kind of metric has received in recent times, we introduce the concept of a G-metric space in any number of variables, and we study some of the basic properties. Then we prove that the family of this kind of metric is closed under finite products. Finally, we show some fixed-point theorems that improve and extend some well-known results in this field.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: 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: 15Citation - Scopus: 13Matkowski Theorems in the Context of Quasi-Metric Spaces and Consequences on g-metric Spaces(Sciendo, 2016) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Samet, BessemIn this paper, we prove the characterization of a Matkowski's theorem in the setting of quasi-metric spaces. As a result, we observe that some recent fixed point results in the context of G-metric spaces are consequences of our main result.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: 3Citation - Scopus: 3On Modified Α-Φ Meir-Keeler Contractive Mappings(Univ Nis, Fac Sci Math, 2014) Salimi, P.; Hussain, N.; Roldan, A.; Karapinar, E.Samet et al. [Nonlinear Anal. 75: 2154-2165, 2012] introduced and studied alpha-psi-contractive mappings. More recently Salimi, et al. [Fixed Point Theory Appl., 2013: 151] modified the notion of alpha-psi-contractive mappings and improved the fixed point theorems in [20, 32]. Here we utilize these notions to establish fixed point results for modified alpha-phi-asymmetric Meir-Keeler contractions and triangular alpha-admissible mappings defined on G-metric and cone G-metric spaces. Several interesting consequences of our theorems are also provided here to illustrate the usability of the obtained results.
