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 ζ : [0,∞) × [0,∞) → R, called the simulation function and the notion of Z-contraction with respect to ζ 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.