Best proximity point results in set-valued analysis
نویسندگان
چکیده
Here we introduce certain multivalued maps and use them to obtain minimum distance between two closed sets. It is a proximity point problem, which is treated here as a problem of finding global optimal solutions of certain fixed point inclusions. It is an application of setvalued analysis. The results we obtain here extend some results and are illustrated with examples. Applications are made to the corresponding single valued cases.
منابع مشابه
Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces
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 $$d(G(x_0),F(x_0))=d(A,B).$$
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تاریخ انتشار 2016