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

Let (X; d) be a metric space and T : X! X be a mapping. In this work, we introduce the mapping : (0;1) (0;1)! R, called the simulation function and the notion ofZ-contraction with respect to 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.