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Generalized minimax inequalities for set-valued mappings. (English) Zbl 1031.49009

Summary: We study generalized minimax inequalities in a Hausdorff topological vector space, in which the minimization and the maximization of a two-variable set-valued mapping are alternatively taken in the sense of vector optimization. We establish two types of minimax inequalities by employing a nonlinear scalarization function and its strict monotonicity property. Our results are obtained under weaker convexity assumptions than those existing in the literature. Several examples are given to illustrate our results.

MSC:

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