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含φ-伪压缩映射的迭代序列等价性问题研究 被引量：3

Study on equivalence of iterative sequences for φ-pseudo contractive mappings
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摘要 在一般的Banach空间中,对不要求Lipschitz连续的φ-伪压缩及φ-增生映射讨论了具误差的Mann迭代与Ishikawa迭代算法的等价性. In this paper, we attempt to prove the equivalence of the convergence between Ishikawa and Mann iterations with errors for φ-pseudo contractive and φ-accretive mappings without Lipschitzian assumptions in general Banach space.
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 2009年第3期15-18,共4页 Journal of Nanchang Institute of Technology
关键词 φ-伪压缩映射 φ-增生映射 MANN迭代 ISHIKAWA迭代 等价性 φ-pseudo contractive mappings 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.

同被引文献26

  • 1Ishikawa S. Fixed points by a new iteration[J]. Proc Amer Math Soc, 1974,44:147- 150.
  • 2Rhoades B E, Stefan M Soltuz. The equivalence of Mann iteration and Ishikawa iteration for φ-uniformly pseudo-contractive[J]. Int J Math Sci ,2004,46:2443 - 2451.
  • 3Chidume C E,Osilike M O. Nonlinear accretive and pseudo-contractive operator equations in Bsnachh spaces[ J]. Nonlinear Anal, 1998, 31:779 - 789.
  • 4Rhoades B E,Stefan M Soltuz. On the equivalence of Mann and Ishikawa iteration methods[J]. Int J Math Sci ,2003:451 -459.
  • 5Rhoades 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.
  • 6Rhoades B E, Stefan M Soltuz,The equivalence between Mann-Ishikawa iterations and muhistep iteration [ J ]. Nonlinear Anal,2004 (58) :219 -228.
  • 7Huang 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.
  • 8Chang 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.
  • 9More C, Nnoli B V C. Iterative solution of nonlinear equations involving set-valude uniformly accretive operators [ J ]. Comput Math Appl,2001 (42) :131 - 140.
  • 10Huang 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.

引证文献3

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南昌工程学院学报
2009年 第3期

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