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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: 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.
