The Applications of Fixed Point Theorems for Multi-Valued Mappings on a Metric Space with a Graph

Abstract

The main purposes of this article are to review some existing fixed point theorems for multi-valued mappings and to introduce the application of these fixed point theorems for a multivalued mappings to the basic knowledge of graph. Let (X,d) be a metric space and T : X 2^X  be a multi-valued mapping. We then obtained sufficient conditions for the fixed point existence of the mapping T in the metric space X endowed with a graph G such that the set V (G) of vertices of G coincides with X and the set of edges of G is
 E (G) = { (x,y) : (x,y) X X }