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