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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:A2 B such that both T and ST are closed and have the KKM property for each Kakutani multimap S:B2 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:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47N10Applications of operator theory in optimization, convex analysis, programming, economics
91A06n-person games, n>2
54C60Set-valued maps (general topology)
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