Coincidence point theorems for graph-preserving multi-valued mappings

Abstract

In this paper, we introduce the concepts of graph-preserving multi-valued mapping and a new type of multi-valued weak G-contraction on a metric space endowed with a directed graph G. We prove some coincidence point theorems for this type of multi-valued mapping and a surjective mapping g : X X under some conditions. Several examples for these new concepts and some examples satisfying all conditions of our main results are also given. Our main results extend and generalize many coincidence point and fixed point theorems in partially ordered metric spaces.