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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:
49J40Variational methods including variational inequalities
54H25Fixed-point and coincidence theorems in topological spaces
49J35Minimax problems (existence)
47H04Set-valued operators
49J53Set-valued and variational analysis