%0 Journal Article %T Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Amini-Harandi, A. %D 2011 %\ 12/15/2011 %V 37 %N No. 4 %P 229-234 %! Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces %K Best proximity pair %K coincidence point %K nonexpansive map %K Hilbert space %R %X 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 $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$ %U http://bims.iranjournals.ir/article_381_ecee2580be42e5630823af4e23482eb7.pdf