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Applications of Fan’s matching theorem in MKKM spaces. (English) Zbl 1499.54167

Summary: Using some concepts in MKKM space, we prove the generalized forms of open and closed versions of Fan’s matching theorem. The \(S\)-weakly KKM multimap is applied to obtain a type of KKM theorem. As an application, a Fan type minimax theorem is proved. Moreover, a minimax inequality is given in these new settings.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
26A51 Convexity of real functions in one variable, generalizations
26B25 Convexity of real functions of several variables, generalizations
55M20 Fixed points and coincidences in algebraic topology
47H10 Fixed-point theorems
54A05 Topological spaces and generalizations (closure spaces, etc.)
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