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Article Citation - WoS: 90Citation - Scopus: 95Common Fixed Points for Single-Valued and Multi-Valued Maps Satisfying a Generalized Contraction in -Metric Spaces(Springer int Publ Ag, 2012) Tahat, Nedal; Aydi, Hassen; Karapinar, Erdal; Shatanawi, WasfiIn this article, we establish some common fixed point theorems for a hybrid pair {} of single valued and multi-valued maps satisfying a generalized contractive condition defined on -metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. 54H25; 47H10; 54E50.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: 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: 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: 37Citation - Scopus: 49A Meir-Keeler Common Type Fixed Point Theorem on Partial Metric Spaces(Springer int Publ Ag, 2012) Aydi, Hassen; Karapinar, ErdalIn this article, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a partial metric space satisfying a generalized Meir-Keeler type contractive condition. The presented theorem extends several well known results in literature.Article Citation - WoS: 11Citation - Scopus: 5A Note on 'n-fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces'(Springer int Publ Ag, 2013) Karapinar, Erdal; Roldan, Antonio; Roldan, Concepcion; Martinez-Moreno, JuanIn this note we prove that a kind of mappings depending on k arguments introduced in (Paknazar et al. in Fixed Point Theory Appl. 2013: 111, 2013) only depend on their first argument. Therefore, results in that paper reduce to the unidimensional case. We also include some commentaries about the different notions of multidimensional fixed point.Article Citation - WoS: 27Citation - Scopus: 32g-β< Type Mappings in g-metric Spaces(Springer int Publ Ag, 2013) Alghamdi, Maryam A.; Karapinar, ErdalIn this paper, we introduce G-beta-psi-contractive mappings which are generalizations of alpha-psi-contractive mappings in the context of G-metric spaces. Additionally, we prove existence and uniqueness of fixed points of such contractive mappings. Our results generalize, extend and improve the existing results in the literature. We state some examples to illustrate our results.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.
