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关于有限族一致渐近φ-伪压缩映象的四种迭代序列收敛的等价性(英文)

The Equivalence of the Convergence of Four Kinds of Iterations for a Finite Family of Uniformly Asymptoticallyφ-pseudocontractive Mappings
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摘要 本文证明了在任意的Banach空间上的关于有限族一致渐进φ-伪压缩映象的具误差的修正Mann迭代过程,具误差的修正Ishikwaw迭代过程,具误差的隐示迭代过程和具误差的合成隐示迭代过程收敛的等价性,其结果推广和改进了Roades,Soltuz和Huang等人的相应结果. In this paper, we prove the equivalences of the strong convergence each other the modified Mann iterative process with errors, the modified Ishikawa iterative process with errors, the implicit iterative process with errors and the composite implicit iterative process with errors for a finite family of uniformly asymptotically Ф-pseudocontractive mappings in arbitrary real Banach space. The results presented in this paper generalize and improve the corresponding results of Roades, Soltuz, and Huang.
作者 王学武
机构地区 山东工商学院数学与信息科学学院
出处 《数学进展》 CSCD 北大核心 2010年第1期79-87,共9页 Advances in Mathematics（China）
关键词 一致渐近Ф-伪压缩映象 合成隐示迭代过程 隐示迭代过程 Ishikwaw迭代过程 MANN迭代过程 等价 uniformly asymptotically Ф-pseudocontractive mapping composite implicit iterative process implicit iterative process Ishikawa iterative process Mann iterative process equivalence
分类号 O177.91 [理学—基础数学]
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参考文献15

  • 1Ishikawa, S., Fixed point and iteration of a nonexpansive mapping in a Banach spaces, Proc. Amer. Ma$h. Soc., 1976, 73: 65-71.
  • 2Mann, W.R., Mean value methods in iteration, Proc. Amer. Math. Soc., 1953, 4: 506-510.
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  • 5Xu H.K., Ori, R.G., An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim.., 2001, 22: 767-773.
  • 6Sun Z.H., Strong convergence of an implicit iteration process for a finite family of asymptotically quasi- nonexpansive mappings, J. Math. Anal. Appl., 2003, 286: 351-358.
  • 7Chang S.S., Tan K.K., et al, On the convergence of implicit iteration process with error for a finit family of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 2006, 313: 273-283.
  • 8Gu F., The new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings, J. Math. Anal. Appl., 2007, 294: 766-776.
  • 9Huang Z.Y., Bu F.W., The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption, J. Math. Anal. Appl., 2007, 325: 586-595.
  • 10Agarwal, R.P., Cho, Y.J, Stability of iterative procedures with errors approximating common fixed points for a couple of qusi-contrative mapping in q-uniformly smooth Banach spaces, J. Math. Anal. Appl., 2002, 272: 435-447.
数学进展
2010年 第1期

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