Generalized minimax inequalities for set-valued mappings
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 employi...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Academic Press
2003
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| Online Access: | http://hdl.handle.net/20.500.11937/33891 |
| Summary: | 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. |
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