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Generalized minimax inequalities for set-valued mappings

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Authors
Li, S.
Chen, G.
Teo, Kok Lay
Yang, X.
Date
2003
Type
Journal Article

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Li, S., and Chen, G., and Teo, K., and Yang, X. 2003. Generalized minimax inequalities for set-valued mappings. Journal of Mathematical Analysis and Applications. 281 (2): pp. 707-723.
Source Title
J. Math. Anal. Appl.
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Faculty
School of Science and Computing
Department of Mathematics and Statistics
Faculty of Science and Engineering
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Copyright © 2003 Elsevier B.V. All rights reserved

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Abstract

In this paper, 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.