Krasnoselskii-type best proximity point theorem in Banach algebras

Abstract

The main purpose of this paper is to present some new existence of hybrid best proximity point theorems involving the sum of two non-self operators
in Banach spaces as well as the product of two non-self operators in Banach algebras. In this way, we extend and revisited the main conclusions of a recent paper by Kar and Veeramani [S. Kar, P. Veeramani, Best proximity version of Krasnoselskii’s fixed point theorem, Acta Sci. Math. (Szeged), 86 (2020), 265-271].
Illustrative examples are given to support our results.