The aim of this paper is to prove the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings defined on generalized metric spaces with a graph. Our results improve and extend several recent results of metric fixed point theory.
In this paper, by using the idea of combining fixed point theory and graph theory, we shall introduce the concept of G-Kannan contraction in a generalized metric space introduced recently by Jleli and Samet, endowed with graph. In this setting, we investigate the existence and uniqueness of the fixed point for mappings satisfying such contraction. This work unifies and generalizes various known comparable results in the literature.
In this paper, we establish fixed point theorems for Chatterjea contraction mappings on a generalized metric space endowed with a graph. Our results extend, generalize, and improve many of existing theorems in the literature. Moreover, some examples and an application to matrix equations are given to support our main result.
In this paper, we give sufficient conditions to ensure the existence of the best proximity point of monotone relatively nonexpansive mappings defined on partially ordered Banach spaces. An example is given to illustrate our results.
We discuss Fisher’s fixed point theorem for mappings defined on a generalized metric space endowed with a graph. This work should be seen as a generalization of the classical Fisher fixed point theorem. It extends some recent works on the enlargement of Banach Contraction Principle to generalized metric spaces with graph. An example is given to illustrate our result.
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