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一致光滑Banach空间中渐近伪压缩映象不动点的迭代逼近 被引量：5

ITERATIVE APPROXIMATION OF FIXED POINTS OF ASYMPTOTICALLY PSEUDO-CONTRACTIVE MAPPINGS IN UNIFORMLY SMOOTH BANACH SPACES
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摘要 本文研究用于逼近一致光滑Banach空间中渐近伪压缩映象不动点的具误差的修改了的Ishikawa 型与Mann型迭代程序的收敛性,改进和发展了文[1]的相应结果及他人的结果. The purpose of this paper is to investigate the convergence of the modified Ishikawa-type and Mann-type iteration processes with errors for approximating fixed points of asymptotically pseudo-contractive mappings in uniformly smooth Banach spaces. The results presented in this paper extend, improve, complement and develop Chang's corresponding ones (see [1]) and others' ones.
作者 曾六川
机构地区 上海师范大学数学系
出处 《数学年刊（A辑）》 CSCD 北大核心 2005年第2期283-290,共8页 Chinese Annals of Mathematics
基金 教育部高等学校优秀青年教师教学和科研奖励基金与上海市曙光计划基金资助的项目.
关键词 不动点 迭代逼近 一致光滑BANACH空间 Asymptotically pseudo-contractive mapping, Fixed point, Iterative approximation, Uniformly smooth Banach space
分类号 O177.91 [理学—基础数学]
  • 相关文献

参考文献10

  • 1曾六川.一致凸Banach空间中非扩张映象的弱收敛定理[J].数学物理学报（A辑）,2002,22(3):336-341. 被引量：7
  • 2Chang, S. S., Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings [J], Proc. Amer. Math. Soc., 129(2000), 845-853.
  • 3Goebel, K. & Kirk, W. A., A fixed point theorem for asymptotically nonexpansive mappings [J], Proc. Amer. Math. Soc., 35(1972), 171-174.
  • 4Schu, J., Iterative construction of fixed points of asymptotically nonexpansive mappings [J], J. Proc. Amer. Math. Soc., 158(1991), 407-413.
  • 5Tan, K. K. & Xu, H. K., Fixed point iteration processes for asymptotically nonexpansive mappings [J], Proc. Amer. Math. Soc., 122(1994), 733-739.
  • 6Zeng, L. C., A note on approximating fixed points of nonexpansive mappings by the Ishikawa iteration process [J], J. Math. Anal. Appl., 226(1998), 245-250.
  • 7曾六川.逼近Banach空间中渐近非扩张映象的不动点[J].数学物理学报（A辑）,2003,23(1):31-37. 被引量：8
  • 8Xu, Z. B. & Roach, G. F., A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations [J], J. Math. Anal. Appl.,167(1992), 340-354.
  • 9Reich, S., Extension problems for accretive sets in Banach spaces [J], J. Funct. Anal.,26(1977), 378-395.
  • 10Reich, S., Product formulas, nonlinear semigroups and accretive operators [J], J. Funct.Anal., 36(1980), 147-168.

二级参考文献2

  • 1Ronald E. Bruck. A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces[J] 1979,Israel Journal of Mathematics(2-3):107～116
  • 2Ronald E. Bruck. A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces[J] 1979,Israel Journal of Mathematics(2-3):107～116

共引文献13

同被引文献39

  • 1向长合.有限个广义渐近拟非扩张型映象公共不动点的逼近[J].重庆师范大学学报（自然科学版）,2006,23(1):6-9. 被引量：3
  • 2唐玉华.序Banach空间中二元算子的不动点的迭代逼近[J].西华师范大学学报（自然科学版）,2006,27(3):293-295. 被引量：2
  • 3向长合.有限个渐近非扩张映象公共不动点的逼近[J].重庆师范大学学报（自然科学版）,2007,24(1):7-10. 被引量：4
  • 4Asplund E. Positivity of duality mappings. Bull Amer. Math. Soc,, 1967, 73: 200-203.
  • 5Chang S S. Some results for asymptotically pseudo-contractive mappings and asymptotically non- expansive mappings. Proc. Amer. Math. Soc., 2001, 129(3): 845-853.
  • 6Goebel K and Kirk W A. A fixed point theorem for asymptotically nonexpansive mappings. Proc. Amer. Math. Soc., 1972, 35(1): 171-174.
  • 7Liu Q H. Iterative sequences for asymptotically quasi-nonexpansive mappings with error member of uniformly convex Banach spaces. J. Math. Anal. Appl., 2002, 266: 468-471.
  • 8Schu J. Iterative construction of fixed points of asymptotically nonexpansive mappings. J. Math. Anal. Appl., 1991, 158: 407-413.
  • 9Chang S S. Some problems and results in the study of nonlinear analysis. Nonlinear Anal. TMA, 1997, 30(7): 4197-4208.
  • 10Gornicki J. Week convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces. Comment Math. Univ. Carolin, 1989, 301: 249-252.

引证文献5

二级引证文献12

数学年刊（A辑）
2005年 第2期

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