| Banach空间中Mann迭代和Ishikawa迭代的等价性问题 |
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| 引用本文： | 王双,柴国庆,胡长松.Banach空间中Mann迭代和Ishikawa迭代的等价性问题[J].应用泛函分析学报,2010,12(3):279-288. |
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| 作者姓名： | 王双 柴国庆 胡长松 |
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| 作者单位： | 1. 盐城师范学院数学科学学院,盐城,224051
2. 湖北师范学院数学系,黄石,435002 |
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| 基金项目： | 国家自然科学基金，湖北省教育厅自然科学基金 |
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| 摘 要： | 用不同于已有的方法证明了任意实Banach空间中一致Lipschitz强连接伪压缩算子在具误差的修正的Mann迭代和具误差的修正的Ishikawa迭代下收敛和稳定的等价性,其中迭代参数{βn}仅需lim sup n→∞βn〈k/L（L＋1）,这推广和改进了目前需假设lim n→∞ βn=0和两迭代程序初始点的取值需相同条件下的已有结果.
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| 关 键 词： | 具误差的修正的Mann迭代序列 具误差的修正的Ishikawa迭代序列 一致Lipschitz映象 强连接伪压缩算子 |
Equivalence problem of Mann and Ishikawa Iterations in Banach Spaces |
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| WANG Shuang,CHAI Guoqing,HU Changsong.Equivalence problem of Mann and Ishikawa Iterations in Banach Spaces[J].Acta Analysis Functionalis Applicata,2010,12(3):279-288. |
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| Authors: | WANG Shuang CHAI Guoqing HU Changsong |
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| Institution: | 1.School of Mathematical Sciences,Yancheng Teachers University,Yancheng 224051 ;2.Department of Mathematics,Hubei Normal University,Huangshi 435002,China) |
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| Abstract: | In this paper,we prove some equivalence theorems between convergence and stability of modified Mann and modified Ishikawa iterative sequence with errors for uniformly Lipschitz strongly successively pseudo-contractive mappings in Banach spaces by using different methods,under the condition on the iteration para-meters limsup lim sup n→∞βn〈k/L（L＋1）.Our results prove and extend the results that need lim n→∞ βn=0 and initial points of two different iteration are the same one. |
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| Keywords: | modified Mann and modified Ishikawa iteration with errors uniformly Lipschitz mappings strongly successively pseudo-contractive mappings |
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