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Constant selections and minimax inequalities. (English) Zbl 1144.54027

The author obtains two constant selection theorems for a map \(S\) whose dual \(S^*\) is upper (respectively lower) semicontinuous. As applications, Fan type matching theorems [cf. Ky Fan, Math. Ann. 266, 519–537 (1984; Zbl 0515.47029)], analytic alternatives and minimax inequalities are obtained.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54C60 Set-valued maps in general topology
49J35 Existence of solutions for minimax problems
52A07 Convex sets in topological vector spaces (aspects of convex geometry)

Citations:

Zbl 0515.47029
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