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 ζ: [0, ∞) × [0, ∞) → R, called the simulation function and the notion of ɀ-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.