Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces (Q1953963)

The paper deals 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 \(F:A\to 2^B\) and \(G:A_0\to 2^{A_0},\) where \(A_0=\{x\in A: \|x-y\|=d(A,B)\text{ for some }y\in B\}\), best proximity pair theorems provide sufficient conditions that ensure the existence of an \(x_0\in A\) such that \[ d(G(x_0),F(x_0))=d(A,B). \]