Fixed points of contractive set valued mappings with set valued domains on a metric space with graph

Abstract

In this article we consider general contractive mappings of the form F : CB(X) ? CB(X), where CB(X) is the set of all nonempty closed and bounded subsets of a complete metric space X endowed with a graph G. We prove some fixed point results for F and discuss how the connectivity of the graph G is related to the fixed points of F.