Theoretical approaches for generalized proximal Z-contraction maps in b-metric spaces with applications

Abstract

This paper explores the simulation function and the concept of Z-contraction concerning ζ, which serve as a generalization of the Banach contraction principle. These ideas unify various existing contraction types by incorporating both d(Ta,Tb) and d(a,b). Our findings extend and generalize the work of Olgun et al. [27], Abbas et al. [1], and Goswami et al. [21], transitioning from metric spaces to the framework of b-metric spaces. We propose the concept of a generalized proximal Z-contraction for pairs of non-self mappings and demonstrate the existence and uniqueness of common best proximity points in complete b-metric spaces. Additionally, we present supporting examples and illustrate some applications of our findings.