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Generalized quasiconvexities, cone saddle points, and minimax theorem for vector-valued functions. (English) Zbl 0826.90102
This paper gives (1) an existence theorem for weak type generalized saddle points; (2) an existence theorem for strong type generalized saddle points and (3) a generalized minimax theorem for a vector-valued function. These theorems are generalizations of the author’s recent results. Some new concepts of convexity and continuity of vector-valued functions are introduced for such generalizations. The proofs of the main theorems, are based on Browder’s coincidence theorem and Tychonoff’s fixed-point theorem.

MSC:
90C29 Multi-objective and goal programming
26B25 Convexity of real functions of several variables, generalizations
26E25 Set-valued functions
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