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Best proximity sets and equilibrium pairs for a finite family of multimaps. (English) Zbl 1169.47040
It is established the existence of a best proximity pair for which the best proximity set is nonempty for a finite family of multimaps whose product is either an ${𝒰}_{c}^{K}$-multimap or a a multimap $T:A\to {2}^{B}$ such that both $T$ and $S\circ T$ are closed and have the KKM property for each Kakutani multimap $S:B\to {2}^{B}$. As an application, existence theorems of equilibrium pairs for free $n$-person games as well as for free 1-person games are proved.

##### MSC:
 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 47N10 Applications of operator theory in optimization, convex analysis, programming, economics 91A06 $n$-person games, $n>2$ 54C60 Set-valued maps (general topology)
##### References:
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