In this paper, we introduce the notions of proximal Berinde g-cyclic contractions of two non-self-mappings and proximal Berinde g-contractions, called proximal Berinde g-cyclic contraction of the first and second kind. Coincidence best proximity point theorems for these types of mappings in a metric space are presented. Some examples illustrating our main results are also given. Our main results extend and generalize many existing results in the literature.

In this paper, we prove existence of a coupled coincidence point theorem and coupled common fixed point theorem for ϕ-contractive mappings in partially ordered complete metric space without the mixed g-monotone property by using the concept of an (F, g)-invariant set. We prove some coupled fixed point theorems for such nonlinear contractive mappings in a complete metric space.Our results are generalization of the results of Wutiphol Sintunavarat, Poom Kumam and Yeol Je Cho (Coupled fixed point theorems for nonlinear contractions without mixed monotone property, Fixed Point Theory and Applications 2012,2012:170.).

In this paper, a new type of non-self-mapping, called Berinde MT-cyclic contractions, is introduced and studied. Best proximity point theorems for this type of mappings in a metric space are presented. Some examples illustrating our main results are also given. Our results generalize and improve some known results in the literature.

In this paper, the existence of best proximity point theorems for two new types of nonlinear non-self mappings in a complete metric space endowed with a directed graph are established. Our main results extend and generalize many known results in the literatures. As a special case of the main results, the best proximity point theorems on partially ordered sets are obtained.

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