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General existence theorems, alternative theorems and applications to minimax problems. (English) Zbl 1192.49015

Summary: We establish general theorems on maximal elements, coincidence points and nonempty intersections for set-valued mappings on GFC-spaces and show their equivalence. Applying them we derive equivalent forms of alternative theorems. As applications, we develop in detail general types of minimax theorems. The results obtained improve or include as special cases several recent ones in the literature.

MSC:

49J40 Variational inequalities
54H25 Fixed-point and coincidence theorems (topological aspects)
49J35 Existence of solutions for minimax problems
47H04 Set-valued operators
49J53 Set-valued and variational analysis
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