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Zbl 1169.47040
Best proximity sets and equilibrium pairs for a finite family of multimaps.
(English)
[J] Fixed Point Theory Appl. 2008, Article ID 457069, 10 p. (2008). ISSN 1687-1812/e

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 ${\cal U}_c^K$-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.
[Sergei V. Rogosin (Minsk)]
MSC 2000:
*47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47N10 Appl. of operator theory in optimization, math. programming, etc.
91A06 $n$-person games, $n>2$
54C60 Set-valued maps

Keywords: fixed point theory; best proximity set; equilibrium pair; Kakutani multimap; KKM-property; $n$-person game

Cited in: Zbl 1219.47081

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