Focusing on best proximity points of generalized versions of cyclic impulsive self-mappings

TL;DR

This paper investigates convergence properties and the existence of best proximity and fixed points for semi-cyclic impulsive self-mappings in metric spaces, extending cyclic mappings to include impulsive and discontinuous behaviors.

Contribution

It introduces a generalized class of semi-cyclic impulsive self-mappings, broadening the scope of fixed point theory to include impulsive and discontinuous mappings in metric spaces.

Findings

Established conditions for convergence of distances

Proved existence and uniqueness of best proximity points

Extended fixed point results to impulsive mappings

Abstract

This paper studies the properties of convergence of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semi-cyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The concept of semi-cyclic self- mappings generalizes the well-known of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as its pre-image. The self-mappings under study may be impulsive since eventually being composite mappings involving two self-mappings, one of them being eventually discontinuous so that the formalism can potentially be applied to the study of stability of a class of impulsive differential equations and their discrete counterparts