Fixed points for Chatterjea contractions on a metric space with a graph

In this work‎, ‎we formulate Chatterjea contractions using graphs in metric spaces endowed with a graph ‎‎and ‎‎‎‎investigate ‎the ‎existence‎ ‎of ‎fixed ‎points ‎for such mappings ‎under two different hypotheses‎. We also discuss the uniqueness of the fixed point. The given result is a generalization of Chatterjea's fixed point theorem from metric spaces to metric spaces endowed with a graph.

Keywords:

‎‎G‎‎-Chatterjea mapping , Fixed point , orbitally ‎‎G‎‎-continuous mapping