The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption (Q854074)
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scientific article; zbMATH DE number 5078949
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption |
scientific article; zbMATH DE number 5078949 |
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The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption (English)
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7 December 2006
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The main result of the paper is included in the title, and, without errors, is a special case of Theorem 5 of the reviewer and \textit{Stefan M. Şoltuz} [J. Math. Anal. Appl. 289, 266--278 (2004; Zbl 1053.47055)]. For maps with bounded range, the definitions of iterations with errors of Xu and Liu are equivalent. Moreover, it is impossible to actually perform the iterations, since the error terms are assumed to be arbitrary. The reviewer hopes to soon see an end to papers dealing with iterations with errors.
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strongly successively pseoudocontractive mappings
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modified Mann iteration with errors
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modified Ishikawa iteration with errors
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