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Lipschitz连续的一致φ-伪压缩映射的等价性

Equivalence of iterative sequences for uniformly φ-pseudocontractive mappings with Lipschitzian assumption
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摘要 在一般的Banach空间中,对Lipschitz连续的一致φ-伪压缩及一致φ-增生映射讨论了具误差的Mann迭代与具误差的Ishikawa迭代算法的等价性,研究结果不要求值域有界且是相关定理的提高. In this paper,we prove the equivalence of the convergence between Ishikawa and Mann iterations with errors for uniformly φ-pseudocontractive and uniformly φ-accretive mappings with Lipschitzian assumptions in general Banach space.The results do not demand that the range be bounded,and improve the related known works.
作者 李小玲 金珍
机构地区 南昌工程学院理学系
出处 《南昌工程学院学报》 CAS 2011年第4期11-14,共4页 Journal of Nanchang Institute of Technology
基金 南昌工程学院青年基金项目(2010KJ024)
关键词 一致φ-伪压缩映射 一致φ-增生映射 MANN迭代 ISHIKAWA迭代 等价性 uniformly φ-pseudocontractive mappings uniformly φ-accretive mappings Mann iterative sequences Ishikawa iterative sequences equivalence
分类号 O177.91 [理学—基础数学]
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参考文献8

  • 1Rhoades B E,Stefan M Soltuz. On the equivalence of Mann and Ishikawa iteration methods[J]. Int J Math Sci ,2003:451 -459.
  • 2Rhoades B E,Stefan M Sohuz. The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators[ J]. Int J Math Sci,2003:2645 - 2651.
  • 3Rhoades B E, Stefan M Soltuz,The equivalence between Mann-Ishikawa iterations and muhistep iteration [ J ]. Nonlinear Anal,2004 (58) :219 -228.
  • 4Huang Zhenyu, Bu Fanwei. The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption[ J]. J Math Anal Appl,2007 (325) :586 -594.
  • 5李小玲,金珍.含φ-伪压缩映射的迭代序列等价性问题研究[J].南昌工程学院学报,2009,28(3):15-18. 被引量：3
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  • 7More C, Nnoli B V C. Iterative solution of nonlinear equations involving set-valude uniformly accretive operators [ J ]. Comput Math Appl,2001 (42) :131 - 140.
  • 8Huang Zhenyu. Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively φ-pseu-docontractive mappings without Lipschitzian assumptions[ J]. J Math Anal Appl,2007 (329) :935 -947.

二级参考文献6

  • 1Rhoades B E,Stefan M.Soltuz.On the equivalence of Mann and Ishikawa iteration methods[J].Int J Math Sci,2003:451-459.
  • 2Rhoades B E,Stefan M.Soltuz.The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators[J].Int J Math Sci,2003:2645-2651.
  • 3Chang S S.On chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces[J].Math Anal Appl,1999,216:94-111.
  • 4Weng X.Fixed point iteration for local strictly pseudocontractive mapping[J].Proc Amer Math Soc,1991,113:727-731.
  • 5Liu L S.Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces[J].Math Anal Appl,1995,194:114-125.
  • 6Berger M S.Nonlinear and functional analysis[M].Academic Press,1977.

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南昌工程学院学报
2011年 第4期

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