Some results on best proximity pair theorems

Abstract

Best proximity pair theorems are considered to expound the sufficient conditions that ensure the existence of an element xo ϵ A, such that d(xo; T xo) = d(A;B) where T : A 2B is a multifunction defined on suitable subsets A and B of a normed linear space E. The purpose of this paper is to obtain best proximity pair theorems directly without using any multivalued fixed point theorem. In fact, the well known Kakutani's fixed point theorem is obtained as a corollary to the main result of this paper.

Keywords

• Best proximity pairs
• Kakutani multifunctions
• Simplicial approximations
• Best approximations