Best proximity points: approximation and optimization

A best proximity point theorem explores the existence of an optimal approximate solution, known as a best proximity point, to the equations of the form Tx = x where T is a non‐self mapping. The purpose of this article is to establish some best proximity point theorems for non‐self non‐expansive mappings, non‐self Kannan‐ type mappings and non‐self Chatterjea‐type mappings, thereby producing optimal approximate solutions to some fixed point equations. Also, algorithms for determining such optimal approximate solutions are furnished in some cases.