Generalization of simulation functions for finding best proximity pair, best proximity point and best proximity coincidence point

Abstract

In the setup of metric spaces, many recent studies established a significant variety of control type mappings and illustrated some fixed point results. In order to represent various contractivity conditions, Khojasteh et al. established the idea of a simulation function and came up with certain fixed-point conclusions. For two nonlinear operators utilizing this type of control function, we explore the existence of the best coincidence proximity point in this study via generalizing the concept of simulation functions.At the end, we applied our results for a new kind of nonlinear integral equations.