Fixed point theorems for Reich type contractions on metric spaces with a graph

Let (X,d)(X,d) be a metric space endowed with a graph GG such that the set V(G)V(G) of vertices of GG coincides with XX. We define the notion of GG-Reich type maps and obtain a fixed point theorem for such mappings. This extends and subsumes many recent results which were obtained for other contractive type mappings on ordered metric spaces and for cyclic operators.