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Minimax theorems for set-valued mappings. (English) Zbl 1054.90086

Authors’ introduction: Minimax problems relative to scalar functions and vector-valued functions have been studied extensively. This paper deals with minimax problems involving set-valued mappings and is organized as follows. In Section 2, we introduce notations and preliminary results; based on these preliminary discussions, a result in C. W. Ha [Math. Ann. 248, 73–77 (1980; Zbl 0413.47042)] is improved. In Section 3, we state two types of minimax theorems for set-valued mappings. In Section 4, we consider other minimax theorems for vector-valued functions, which improve partially the results in F. Ferro [J. Optim. Theory Appl. 60, 19–31 (1989; Zbl 0631.90077) and 68, No. 1, 35–48 (1991; Zbl 0696.90061)].

MSC:

90C47 Minimax problems in mathematical programming
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