Fixed point theorems for graph preserving multivalued mappings in complete metric spaces with graph

Abstract

In this paper, we introduce a new type of graph-preserving multivalued mappings in a complete metric space endowed with a directed graph and prove some fixed point theorems under some contractive conditions related to a Reich type contraction. We also give some examples supporting our main results. The main results obtained in the paper extend and generalize many results in the literature.