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

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 o 2^ B and G:A_0 o 2^{A_0}, where A_0={xin A: ||x-y||=d(A,B) for some y in B}, best proximity pair theorems provide sufficient conditions that ensure the existence of an x 0 in A such that d(G(x 0),F(x 0))=d(A,B).