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Banach空间中Ishikawa迭代序列的稳定性和收敛性问题 被引量：3

Stability and Convergence Problem of Ishikawa and Mann Iterative Sequences in Banach Spaces
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摘要 在Banach空间的框架下,讨论了中间意义下的渐进非扩张的渐进伪压缩的具平均误差的修正的Ishikawa和Mann迭代序列的收敛性和稳定性之间的等价性问题,改进和推广了以前的结果. Some equivalence theorems between convergence and stability of modified Ishikawa and modified Mann iterative sequences with mean errors for asymptotically nonexpansive mappings in the intermediate sense and asymptotically pseudocontractive mappings in Banach spaces are obtained, the results presented in this paper extend and improve some recent results.
作者 张石生
机构地区 宜宾学院数学系
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2007年第5期1051-1062,共12页 Acta Mathematica Sinica：Chinese Series
关键词 具平均误差的修正Ishikawa(Mann)迭代序列 渐近非扩张映象 中间意义的渐进非扩张映象 modified Ishikawa and modified Mann iteration with mean errors asymptotically nonexpansive mapping asymptotically nonexpansive mapping in the intermediate sense
分类号 O177.91 [理学—基础数学]
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参考文献22

  • 1Chang S. S., Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mapping, Proc. Amer. Math. Soc., 2001, 129(3): 845-853.
  • 2Chang S. S., Cho Y. J., Kim J. K., The equivalence between the convergence of modified Picard, Modified Mann and modified Ishikawa iterations, Math. Computer Modelling, 2003, 37: 985-991.
  • 3Chang S. S., Lee W. H. J., Tan K. K., Stability and convergence of modified Ishikawa iterative sequences with errors in Banach spaces, Acta Math. Hungar., 2006, 110(4): 267-285.
  • 4Rhoades B. E., Soltuz S. M., On the equivalence of Mann and Ishikawa iteration methods, Internat. J. Math. Math. Sci., 2003: 451-459.
  • 5Rhoades B. E., Soltuz S. M., The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators, J. Math. Math. Sci., 2004: 2645-2651.
  • 6Rhoades B. E., Soltuz S. M., The equivalence between the convergence of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps, J. Math. Anal. Appl., 2004, 289:266-278.
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  • 10Browder F. E., Nonexpansive nonlinear operators in Banach spaces, Proc. Natl. Acad Sci. USA, 1965, 54: 1041-1044.

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数学学报（中文版）
2007年 第5期

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