3种迭代的收敛的等价性(Ⅱ)

  • 郑亚勤 ,
  • 石金玮 ,
  • 周海云
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  • 1.河北大学数学与计算机学院,河北,保定,071002;河北农业大学,理学院,河北,保定,071001; 2.华北电力大学,河北,保定,071051; 3.华北电力大学,非线性分析研究所,河北,保定,071003

网络出版日期: 2007-01-25

基金资助

国家自然科学基金

Equivalence Among the Convergence of Three Kinds of Iterations(Ⅱ)

  • ZHENG Ya-qin ,
  • SHI Jin-wei ,
  • ZHOU Hai-yun
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Online published: 2007-01-25

摘要

若T是强逐次伪压缩映射时,则三种迭代(改进的Mann迭代,改进的Ishikawa迭代和改进的三重迭代)的收敛性是等价的.

本文引用格式

郑亚勤 , 石金玮 , 周海云 . 3种迭代的收敛的等价性(Ⅱ)[J]. 河北大学学报(自然科学版), 2007 , 27(1) : 1 -3 . DOI: 10.3969/j.issn.1000-1565.2007.01.002

参考文献

[1] 石金玮, 郑亚勤, SHI Jin-wei, ZHENG Ya-qin. 3种迭代收敛的等价性 [J]. 河北大学学报(自然科学版) 2005.doi:10.3969/j.issn.1000-1565.2005.01.005
[2] MANN W R. Mean value in iteration [J]. Amer Math Soc 1953, 4.
[3] ISHIKAWA S. Fixed points by new iteration method [J]. Proceedings of the American Mathematical Society 1974, 44.
[4] Rhoades BE., Soltuz SM.. The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps [J]. Journal of Mathematical Analysis and Applications 2004, 1(1).
[5] Noor MA., Rassias TM., Huang ZY.. Three-step iterations for nonlinear accretive operator equations [J]. Journal of Mathematical Analysis and Applications 2002, 1(1).
[6] WENG X. Fixed point iteration for local strictly pseudocontractive mapping [J]. Proceedings of the American Mathematical Society 1991, 113.
[7] Morales CH., Jung JS.. Convergence of paths for pseudo-contractive mappings in Banach spaces [J]. Proceedings of the American Mathematical Society 2000, 11(11).
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