(C , Ψ * , G ) Class of Contractions and Fixed Points in a Metric Space Endowed with a Graph

Abstract

In this paper, we introduce the (C,Ψ∗,G) class of contraction mappings using C-class functions and some improved control functions for a pair of set valued mappings as well as a pair of single-valued mappings, and prove common fixed point theorems for such mappings in a metric space endowed with a graph. Our results unify and generalize many important fixed point results existing in literature. As an application of our main result, we have derived fixed point theorems for a pair of α -admissible set valued mappings in a metric space.