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.
