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 $$d(G(x_0),F(x_0))=d(A,B).$$
Amini-Harandi, A. (2011). Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces. Bulletin of the Iranian Mathematical Society, 37(No. 4), 229-234.
MLA
A. Amini-Harandi. "Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces". Bulletin of the Iranian Mathematical Society, 37, No. 4, 2011, 229-234.
HARVARD
Amini-Harandi, A. (2011). 'Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces', Bulletin of the Iranian Mathematical Society, 37(No. 4), pp. 229-234.
VANCOUVER
Amini-Harandi, A. Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces. Bulletin of the Iranian Mathematical Society, 2011; 37(No. 4): 229-234.
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