The equivalence between the convergence of modified Picard, modified Mann, and modified Ishikawa iterations (Q597557)
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scientific article; zbMATH DE number 2082773
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The equivalence between the convergence of modified Picard, modified Mann, and modified Ishikawa iterations |
scientific article; zbMATH DE number 2082773 |
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The equivalence between the convergence of modified Picard, modified Mann, and modified Ishikawa iterations (English)
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6 August 2004
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The authors consider equivalence between the convergence for the modified Picard iteration, the modified Mann iteration, and the modified Ishikawa iteration. All those modified iterations are for \(L\)-Lipschitz mappings, Banach contractive mappings, nonexpansive mappings, and asymptotically nonexpansive mappings in Banach spaces. Some conditions related to positive series are proved to be sufficient for the mentioned equivalence.
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uniformly \(L\)-Lipschitzian mapping
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asymptotically non-expansive mapping
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non-expansive mapping
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