A further improvement of a minimax theorem of Borenshtein and Shul'man (Q2764709)
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scientific article; zbMATH DE number 1690878
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A further improvement of a minimax theorem of Borenshtein and Shul'man |
scientific article; zbMATH DE number 1690878 |
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2001
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minimax theorem
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quasi-concavity
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A further improvement of a minimax theorem of Borenshtein and Shul'man (English)
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The author gives an interesting improvement on a minimax theorem by \textit{O. Yu. Borenshtejn} and \textit{V. S. Shul'man} [Math. Notes. 50, No. 1, 752-754 (1991); translation from Mat. Zametki 50, No. 1, 139--141 (1991; Zbl 0739.49006)] The conditions ensuring the validity of the following equality NEWLINE\[NEWLINE \sup_{\lambda \in I}\inf_{x\in X}f(x,\lambda)=\inf_{x\in X}\sup_{\lambda \in I}f(x,\lambda) NEWLINE\]NEWLINE were weakened. Mainly, the concavity of \(f(x,\cdot)\) is replaced by quasi-concavity.
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