Springer and the Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 420111215Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces229234381ENA.Amini-HarandiJournal Article20100210This paper is concerned with the best proximity pair problem in <br />Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space <br />$H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, <br />where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin <br />B}$, best proximity pair theorems provide sufficient conditions <br />that ensure the existence of an $x_0in A$ such that <br />$$d(G(x_0),F(x_0))=d(A,B).$$http://bims.iranjournals.ir/article_381_ecee2580be42e5630823af4e23482eb7.pdf