Document Type : Research Paper

Authors

• Kamal Fallahi
• Aris Aghanians

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Abstract

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