A New Approach to the Study of Fixed Point Theory for Simulation Functions

Abstract

Let (X,d) be a metric space and T: X-> X be a mapping. In this work we introduce the mapping \zeta\:[0,\infty).[0,\infty)->R, called the simulation function and the notion of Z-contraction with respect to \zeta which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx,Ty) and d(x,y). The related fixed point theorems are also proved.