Some fixed point theorems for G-nonexpansive mappings on ultrametric spaces and non-Archimedean normed spaces with a graph

Abstract

A very interesting approach in the theory of fixed point is some general structures was recently given by Jachymski by using the context of metric spaces endowed with a graph. The purpose of this article is to present some new fixed point results for G-nonexpansive mappings defined on an ultrametric space and non-Archimedean normed space which are endowed with a graph. In particular, we investigate the relationship between weak connectivity graph and the existence of fixed point for these mappings. AMS Subject Classification: 47H10, 32P05.