Fixed points of mappings defined on a ball of a reflexive Banach space (Q2746994)
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scientific article; zbMATH DE number 1657015
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fixed points of mappings defined on a ball of a reflexive Banach space |
scientific article; zbMATH DE number 1657015 |
Statements
26 February 2002
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fixed point
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nonexpansive map
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finite-dimensional reduction
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0.91365695
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Fixed points of mappings defined on a ball of a reflexive Banach space (English)
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The author generalizes Altman's fixed point theorem to the case of reflexive Banach spaces: Let \(X\) be a reflexive Banach space and let \(f\) be a mapping from \(B_r:=\{x\in X|\;\|x\|\leq r\}\) to \(X\) which is continuous in the weak topology. If \(\|fx\|\leq\max\{\|fx-x\|,r\}\) whenever \(\|x\|=r\) then \(f\) has a fixed point. The proof is obtained by a straightforward finite-dimensional reduction.
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