Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in hilbert spaces

Abstract

This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets A and B of a Hilbert space H and the set-valued maps F: A → 2 B and G: A 0 → 2 A0, where A 0 = {x ∈ A: {norm of matrix}x - y{norm of matrix} = d(A,B) for some y ∈ B}, best proximity pair theorems provide sufficient conditions that ensure the existence of an x 0 ∈ A such that d(G(x 0), F(x 0)) = d(A,B). © 2011 Iranian Mathematical Society.