The Denjoy-Wolff theorem for \(s\)-condensing mappings (Q2769206)
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scientific article; zbMATH DE number 1701105
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Denjoy-Wolff theorem for \(s\)-condensing mappings |
scientific article; zbMATH DE number 1701105 |
Statements
5 February 2002
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Denjoy-Wolff theorem
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convergence of iterates
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holomorphic maps
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condensing maps
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Kobayashi distance
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nonexpansive maps
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fixed-point free maps
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The Denjoy-Wolff theorem for \(s\)-condensing mappings (English)
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Let \(f\) be a holomorphic self-map of the open unit ball in a strictly convex Banach space. It is shown that if \(f\) is a fixed-point free set contraction with respect to the Kuratowski measure of noncompactness, then the iterates converge locally uniformly to a constant map with values on the boundary. A similar result is obtained for semigroups which are nonexpansive with respect to the Kobayashi distance.
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