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一致凸 Banach空间中渐近非扩展映象的迭代格式之新强收敛定理(英文) 被引量：4

Some New Strong Convergence Theorems for Iterative Schemes for Asymptotically Nonexpansive Mappings in Uniformly Convex Banach Spaces
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摘要 通过使用新的分析技巧 ,建立了 (关于 )渐近非扩展映象的修正的迭代格式的强收敛定理 .所得结果改进了 Schu,Rhoades以及其他作者相关的结果 . In the present paper, by virtue of newanalysis technique, we have established a new strong convergence theorem for themodified Mann iteration scheme for a class of asymptotically nonexpansive mappi ngs in uniformly convex Banach spaces. Our results improve the recent ones annou nced by Schu, Rhoades and others.
作者 周海云 高改良 陈东青
机构地区 石家庄机械工程学院数学系
出处 《应用泛函分析学报》 CSCD 2003年第3期234-239,共6页 Acta Analysis Functionalis Applicata
关键词 凸Banach空间 渐近非扩展映象 迭代格式 强收敛定理 asymptotically nonexpansive mapping modified Manniteration scheme uniformly convex Banach space
分类号 O177.2 [理学—基础数学]
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参考文献13

  • 1[1]Goebel K, Kirk W A. A fixed point theorem for asymptotically non-expansive mappings[J]. Proc Amer Math Soc, 1972, 35: 171-174.
  • 2[2]Schu J. Iterative construction of fixed points of asymptotically nonexpansive mappings[J]. J Math Anal Appl, 1991, 158: 407-413.
  • 3[3]Schu J. Weak and strong convergence of fixed points of asymptotically nonexpansive mappings[J]. Bull Austral Math Soc, 1991, 43: 153-159.
  • 4[4]Tan K K, Xu H K. Fixed point iteration processes for asymptotically nonexpansive mappings[J]. Proc Amer Math Sco, 1994, 122: 733-739.
  • 5[5]Xu H K. Inequalities in Banach spaces with applications[J]. Nonlinear Anal, 1991, 16: 1127-1138.
  • 6[6]Rhoades B E. Fixed point iterations for certain nonlinear mappings[J]. J Math Anal Appl, 1994, 183:118-120.
  • 7[7]Liu Q H, Xue L X. Convergence theorems of iterative sequences for asymptotically nonexpansive mapping in a uniformly convex Banach space[J]. J Math Res and Exp, 2000, 20: 331-336.
  • 8[8]Tan K K, Xu H K. Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process[J]. J Math Anal Appl, 1993, 178: 301-308.
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同被引文献7

  • 1王绍荣.渐近非扩展映象的具误差的Ishikawa迭代序列的新强收敛定理[J].应用泛函分析学报,2004,6(2):187-192. 被引量：1
  • 2王学武.一致凸Banach空间非扩张映象带误差的Ishikawa型的三重迭代序列的收敛性[J].大学数学,2007,23(1):56-60. 被引量：2
  • 3Schu J. Iterative construction of fixed points of asymptotically nonexpansive mappings[J]. J Math Anal Appl, 1991, 158: 407-413.
  • 4Rhoades B E. Fixed Point iterations for certain nonlinear mappings[J]. J Math Anal Appl, 1994, 183:118-120.
  • 5Schu J. Weak and strong convergence to fixed points of asymptotically nonexpansive mappings[J]. Bull Austral Math, Soc, 1991, 43: 153-159.
  • 6Zeqing Liu. Iterative approxmation of fixed points for generalized asymptotically contractive and generalized hemicontractive mappings[J]. Pan-American Math Journal, 2002, 12(4): 67-74.
  • 7Tan K K, Xu H K. Iterative solution to nonlinear equations of strongly accretive operators in Banach spaces[J]. J Math Anal Appl, 1993, 178: 9-21.

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应用泛函分析学报
2003年 第3期

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