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一致凸B空间中非扩张映象具误差的Ishikawa迭代过程的收敛性 被引量：1

Convergence of Ishikawa Iteration Process with Errors for Nonexpansive Mapping in A Uniformly Convex B-space
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摘要 利用一致凸Banach空间中凸性模的性质和对偶映射在任意有界集的一致连续性,研究了非扩张映象具误象的Ishikawa迭代过程的收敛性问题.得出具误差的Ishikawa迭代序列强收敛和弱收敛的某些充分条件.主要结果改进并完善了前期研究者的相应成果. By using the properties of the convexity module and uniform coninuity of the duality maps on any bounded sets in a uniformly convex Banach space, we discussed convergence problems of the Ishikawa iteration proces with errors for nonexpansive mappings. In a uniformly convex Banach space some sufficient conditions of strongly and weakly convergence theorems of Ishikawa iterative sequences with errors are given. Our main results improve and extend the corresponding results in the references.
作者 张文良 侯志彬 何震
机构地区 河北金融学院基础部 河北大学数学与计算机学院
出处 《河北大学学报（自然科学版）》 CAS 北大核心 2007年第4期352-356,共5页 Journal of Hebei University(Natural Science Edition)
基金 河北省自然科学基金资助项目(A2006000941) 教育部科学技术研究重点支持项目(207014)
关键词 带误差的Ishikawa迭代序列 非扩张映象 一致凸Banach空间的凸性模. Ishikawa iterative sequence with errors nonexpansive mapping the convexity module of a uniformly comvex Banach spse
分类号 O175 [理学—基础数学]
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参考文献8

  • 1XU YUGUANG.Ishikawa Mann iterative process with errors for nonlinear strongly accretive operater equations[J].Math Anal Appl,1998,224:91-101.
  • 2OPIAL Z.Weak convergence of sequence of successive approximations for nonexpansive mappings[J].Bull Amer Math Soc,1967,73:595-597.
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  • 4KOK-KEONG TAN,HONG-KUN XU.Approsimationg fixed points of nonexpansive mappings by the Ishikawa iteration process[J].J Mathe Anal Appl,1993,178:301-308.
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同被引文献12

  • 1曾六川.Banach空间中Reich-Takahashi迭代法的强收敛定理[J].数学学报（中文版）,2005,48(3):417-426. 被引量：6
  • 2Goebel K, Kirk W A. A fixed point theorem for asymptotically nonexpansive mappings [J]. Proc Amer Math Soc, 1972, 35(1): 171-174.
  • 3Kirk W A. Fixed point theorem for non-Lipschitzian mappings of asymptotically nonexpansive type [J]. Israel J Math, 1974, 17(4): 339-346.
  • 4Zeng Luchuan. A note on approximating fixed points of nonex- pansive mapping by the Ishikawa iterative processs [J]. J Math Anal Appl, 1998, 226(1): 245-250.
  • 5Chang Shishen, Cho Y J, Kim J K, et al. Iterative approximation of fixed points for asymptotically nonexpansive types mappings in Banach space [J]. Pan-American Mathematical Journal, 2001, 11(3): 53-63.
  • 6Sun Zhaohong, He Chang. Iterative approximation of fixed points for asymptotically nonexpansive types mappings with er- ror member [J]. Acta Mathematica Sinica, chinese series, 2004, 47(4): 811-818.
  • 7Xu Hongkun. Inequalities in Banach space with applications [J]. Nonlinear Anal TMA, 1991, 16(12): 1127-1138.
  • 8Chang Shishen. Some problems and results in the study of nonlinear analysis [J]. Nonlinear Anal TMA, 1997, 30(7): 4197- 4208.
  • 9赵良才,张石生.Banach空间中渐近非扩张映象具误差的强收敛定理[J].数学学报（中文版）,2008,51(1):99-108. 被引量：7
  • 10孟京华.Banach空间中具有数列的渐近拟非扩张型映象的不动点及其具有误差的Ishikawa迭代逼近[J].高等学校计算数学学报,2008,30(3):193-200. 被引量：2

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河北大学学报（自然科学版）
2007年 第4期

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