Best Proximity Points

Abstract

Ky Fan’s best approximation theorems, best proximity pair theorems, and best proximity point theorems have been studied in the literature when the fixed point equation \(Tx = x\) does not admit a solution. This chapter contains some basic results on best proximity points of cyclic contractions and relatively nonexpansive maps. An application of a best proximity point theorem to a system of differential equations has been discussed. Though it is not possible to include all the available interesting results in best proximity points, an attempt has been made to introduce some results involving best proximity points and references of related work have been indicated.