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On existence of equilibrium pair for constrained generalized games. (English) Zbl 1091.47060

A best proximity pair theorem is proved for given nonempty subsets \(A\) and \(B\) of a normed linear space \(X\) and a Kakutani set-valued mapping \(T: A\to 2^B\). The existence of an equilibrium pair for constrained generalized games is also obtained under some conditions.

MSC:

47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
91B50 General equilibrium theory
91A99 Game theory
47H10 Fixed-point theorems
47H04 Set-valued operators
54H25 Fixed-point and coincidence theorems (topological aspects)
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