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Best proximity pairs and equilibrium pairs for Kakutani multimaps. (English) Zbl 1225.47056

Summary: New existence theorems of best proximity pairs for a finite family of Kakutani multimaps are proved in a normed space setting. As applications, new existence theorems of equilibrium pairs for free \(n\)-person and 1-person games are obtained. Our results generalize and improve several well-known results.

MSC:

47H04 Set-valued operators
54H25 Fixed-point and coincidence theorems (topological aspects)
91A06 \(n\)-person games, \(n>2\)
41A50 Best approximation, Chebyshev systems
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