一致L-Lipschitz的渐近伪压缩映象不动点的Ishikawa迭代逼近问题

王绍荣;王彭德;杨泽恒;熊明

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (9) : 1206-1213.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (9) : 1206-1213. DOI: 10.12341/jssms09259
论文

一致L-Lipschitz的渐近伪压缩映象不动点的Ishikawa迭代逼近问题

    王绍荣, 王彭德, 杨泽恒, 熊明
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Iterative Approximation Problem of Fixed Points for Uniformly L-Lipschitz and Asymptotically Pseudocontractive Mappings

    WANG Shaorong, WANG Pengde, YANG Zeheng, XIONG Ming
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摘要

在任意实的Banach空间中研究了用具误差的修正的Ishikawa与Mann迭代程序来逼近一致L-Lipschitz的渐近伪压缩映象不动点的强收敛性问题,在去掉条件∑n=0∞αn2<∞,\q∑n=0∞γn<∞,\q∑n=0∞αn(βn+δn)<∞,\q∑n=0∞αn(kn−1)<∞
之下,证明了相关文献的结果仍然成立.所得结果不但改进和推广了最近一些人的最新结果,而且也从根本上改进了定理的证明方法.

Abstract

The purpose of this paper is to investigate the strong convergence of the modified Ishikawa and Mann iterative processes with errors for approximating fixed points of uniformly L-Lipschitz and asymptotically pseudocontractive mappings in an arbitrary real Banach space. By removing the restriction
∑n=0∞αn2<∞,\q∑n=0∞γn<∞,\q∑n=0∞αn(βn+δn)<∞,\q∑n=0∞αn(kn−1)<∞,
it is proven that the relevant results remain true. The results presented in this paper improve and extend some recent existing results.

关键词

一致L-Lipschitz的渐近伪压缩映象 / 具误差的修正的Ishikawa迭代序列 / 不动点.

Key words

L-Lipschitz asymptotically pseudocontractive mapping / modified Ishikawa iterative sequence with errors / fixed point.

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王绍荣 , 王彭德 , 杨泽恒 , 熊明. 一致L-Lipschitz的渐近伪压缩映象不动点的Ishikawa迭代逼近问题. 系统科学与数学, 2010, 30(9): 1206-1213. https://doi.org/10.12341/jssms09259
WANG Shaorong , WANG Pengde , YANG Zeheng , XIONG Ming. Iterative Approximation Problem of Fixed Points for Uniformly L-Lipschitz and Asymptotically Pseudocontractive Mappings. Journal of Systems Science and Mathematical Sciences, 2010, 30(9): 1206-1213 https://doi.org/10.12341/jssms09259
中图分类号： 47H05    47H10    47H15   
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