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具随机性误差隐迭代程序的收敛性 被引量：2

Convergence of Implicit Iteration Process with Random Errors
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摘要 在任意Banauch空间中,证明了有限族渐近半压缩映象具随机性误差的隐迭代程序逼近其公共不动点的强收敛性定理.所得结论推广和改进了引文中的相应结果. In this paper, strong convergence theorems for approximation of common fixed points of a finite family of asymptotically demicontractive mappings are proved in an arbitrary Banach space using an implicit iteration scheme with random errors. Our results of this paper improve and extend the corresponding results.
作者 杨理平 胡刚
机构地区 广东工业大学应用数学学院 广东工业大学机电工程学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2008年第1期11-22,共12页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金(60674098) 广东省自然科学基金(重点)资助项目(06104659；5001798)
关键词 渐近半压缩映象 具随机性误差的隐迭代序列 半紧 asymptotically demicontractive mappings implicit iterative sequence with random errors demicompact
分类号 O177.91 [理学—基础数学]
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参考文献19

  • 1Goebel K., Kirk W. A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 1972, 35: 171-174.
  • 2Schu J., On a theorem of C. E. Chidume concerning the iterative approximation of fixed points, Math. Nachr., 1991, 153: 407-413.
  • 3Goebel K., Kirk W. A., A fixed point theorem for tansformations whose itertes have uniform Lipschitz constant, Studia Math., 1973, 47: 135-140.
  • 4Liu Q. H., Convergence Theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings, Nonlinear Anal., 1996, 26: 1835-1842.
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  • 7Osilike M. O., Aniagbosor S. G., Akuchu B. G., Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces, Panamer. Math. J., 2002, 12(2): 77-88.
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  • 10Osilike M. O., Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl., 2004, 294: 73-81.

同被引文献25

  • 1Goebel K, Kirk W A. A fixed point theorem for asymptotically nonexpansive mappings. Proc Amer Math Soc, 1972, 35:171-174.
  • 2Bruck R E, Kuczumow T, Reich S. Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property. Colloquium Mathematicum, 1993, LXV(2): 169-179.
  • 3Kirk W A. Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type. Israel J Math, 1974, 17:339 346.
  • 4Alber YA I, Chidume C E, Zegeye H. Approximating fixed points of total asymptotically nonexpansive mappings. Fixed Point Theory Appl, 2006, (2006): 10673.
  • 5Shahzad N, Zegeye H. Strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi-nonexpansive maps. Appl Math Comput, 2007, 189:1058-1065.
  • 6Schu J. Iterative construction of fixed points of asymptotically nonexpansive mappings. J Math Anal Appl, 1991, 158:407 -413.
  • 7Schu J. Weak and strong convergence of fixed points of asymaptotically nonexpansive mappings. Bull Austral Math Soc. 1991.43:153-159.
  • 8Tan K K, Xu H K. Fixed point iteration processes for asymptotically nonexpansive mappings. Proc Amer Math Soc, 1994, 122:733-739.
  • 9Xu H K. Existence and convergence for fixed points of mappings of asymptotically nonexpansive type. Nonlinear Anal, 1991, 16:1139-1146.
  • 10Osilike M O, Aniagbosor S C. Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings. Math Comput Modelling, 2000, 32(10): 1181-1191.

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数学学报（中文版）
2008年 第1期

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