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On some equilibrium problems for multimaps. (English) Zbl 0990.49003
Summary: In this paper, we first establish the continuity property for multimaps and generalized Berge’s theorem for multimaps. Then we apply these results, and the Fan-Browder fixed point theorem, to establish the existence theorems of quasi-equilibrium problems and generalized quasi-equilibrium problems for multimaps.

MSC:
49J35 Existence of solutions for minimax problems
90C47 Minimax problems in mathematical programming
49J40 Variational inequalities
49J53 Set-valued and variational analysis
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