%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 Springer and the 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