The Knaster--Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications (Q1961314)
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scientific article; zbMATH DE number 1389681
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Knaster--Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications |
scientific article; zbMATH DE number 1389681 |
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The Knaster--Kuratowski and Mazurkiewicz theory in hyperconvex metric spaces and some of its applications (English)
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2000
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The authors give a characterization of the Knaster--Kuratowski--Mazurkiewicz principle in hyperconvex metric spaces. As applications, they give hyperconvex versions of Fan's minimax principle and Fan's best approximation theorem for set-valued mappings. In particular, the Browder--Fan and Schauder--Tychonoff fixed point theorems are extended in hyperconvex metric spaces. Finally, existence theorems for saddle points, intersection theorems and Nash equilibria in hyperconvex metric spaces are obtained.
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hyperconvex space
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fixed point
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saddle point
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nonexpansive map
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Nash equilibria
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