| The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space |
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| 引用本文： | Liping Yang. The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space[J]. 高等学校计算数学学报(英文版), 2007, 16(1): 83-91 |
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| 作者姓名： | Liping Yang |
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| 作者单位： | Liping Yang Faculty of Applied Mathematics，Guangdong University of Technology，Guangdong 510090，China. |
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| 摘 要： | Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method, it is proved that the convergence of Mann, Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration. The results of this paper extend the results of Rhoades and Soltuz in some aspects.
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| 关 键 词： | Φ-strongly accretive operator Φ-strongly pseudocontractive operator continuous Mann iteration Ishikawa iteration multistep iteration. |
| 收稿时间： | 2005-06-08 |
| 修稿时间： | 2006-02-16 |
The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space |
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| Liping Yang. The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space[J]. Numerical Mathematics A Journal of Chinese Universities English Series, 2007, 16(1): 83-91 |
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| Authors: | Liping Yang |
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| Abstract: | Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method,it is proved that the convergence of Mann,Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration.The results of this paper extend the results of Rhoades and Soltuz in some aspects. |
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| Keywords: | Φ-strongly accretive operator Φ-strongly pseudocontractive operator continuous Mann iteration Ishikawa iteration multistep iteration |
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