Fixed point of set-valued graph contractions in metric spaces

Abstract

In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $T$ be a multivalued mappings on $X.$ Among other things, we obtain a fixed point of the mapping $T$ in the metric space $X$ endowed with a graph $G$ such that the set of vertices of $G,$ $V(G)=X$ and the set of edges of $G,$ $E(G)subseteq Xtimes X.$