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Banach空间中有限渐近拟非扩张映射族的收敛定理 被引量：4

Convergence Theorems for a Finite Family of Asymptotically Quasi-Nonexpansive Mappings
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摘要 在一致凸的Banach空间中引入了一类有限渐近拟非扩张映射族,研究了此类非扩张映射的多步Ishikawa型迭代序列,证明了此迭代序列在一定条件下强收敛到有限渐近拟非扩张映射族的公共不动点. In this article we introduce a finite family of asymptotically quasi-nonexpansive mappings in a u niformly convex Banach space. Under certain conditions, we study a multi-step Ishikawa-type iteration se quence and prove that the sequence strongly converges to a common fixed point for the finite family of as ymptotically quasi-nonexpansive mappings.
作者 肖鹃 谢荣华 邓磊
机构地区 西南大学数学与统计学院
出处 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2014年第2期87-91,共5页 Journal of Southwest University(Natural Science Edition)
基金 国家自然科学基金资助项目(11226228) 河南省教育厅自然科学研究项目(2011B110025) 河南省科技发展计划项目(122300410256)
关键词 BANACH空间 渐近非扩张映射 渐近拟非扩张映射 Banach space asymptotically nonexpansive mapping asymptotically quasi-nonexpansive mapping
分类号 O177.2 [理学—基础数学]
  • 相关文献

参考文献7

  • 1CHIDUME C E, SHAHZAD N. Strong Convergence of an Implicit Iteration Process for a Finite Family of Nonexpansive Mappings EJ:. Nonlinear Anal, 2005, 62(6): 1149-1156.
  • 2CHIDUME C E, ALI B. Weak and Strong Convergence Theorems for Finite Families of Asymptotically Nonexpansive Mappings in Banach Spaces EJ:. J Math Anal Appl, 2007, 330(1): 377-387.
  • 3RHOADES B E, SOLTUZ S M. The Equivalence Between Mann-Ishikawa Iterations and Multi-Step Iteration [J]. Non- linear Anal, 2004, 58(1/2): 219-228.
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  • 7王莹,邓璎函.2个有限渐近非扩张映射族的迭代序列的强收敛性[J].西南大学学报（自然科学版）,2011,33(8):129-133. 被引量：1

二级参考文献11

  • 1GOEBEL K. A Fixed Point Theorem for Asymptotically Nonexpansive Mappings [J]. Proc Amer Math Soc, 1972, 35:171-174.
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同被引文献22

  • 1郭大钧,孙经先.Banach空间常微分方程理论的若干问题[J].数学进展,1994,23(6):492-504. 被引量：10
  • 2周友明.Banach空间中二阶微分方程的周期边值问题[J].应用数学学报,2006,29(3):436-444. 被引量：11
  • 3LI Wei, CHO Y J. Iterative Schemes for Zero Points of Maximal Monotone Operators and Fixed Points of NonexpansiveMappings and Their Applications [J]. Fixed Point Theory Appl, 2008,2008 : 1 — 8.
  • 4TAKAHASHI W. Nonlinear Functional Analysis [M], Yokohama: Yokohama Publishers, 2000.
  • 5QIN Xiao-long, SU Yong-fu. Strong Convergence Theorems for Relatively Nonexpansive Mappings in a Banach Space EJ-]. Nonlinear Anal, 2007, 67(6): 1958-1965.
  • 6ZHOU Hai-yun, GAO Xing-hui. An Irerative Method of Fixed Points for Closed and Quasi-strict Pseudo-contractions in BanachSpaces _-J~. J ApplMathComput, 2010, 33(1-2): 227-237.
  • 7XU B L, NOOR M A. Fixed-Point Iterations for Asymptotically Nonexpansive Mapppings in Banach Spaces [J]. Math Anal Appl, 2002, 267(2): 444-453.
  • 8SHAHZAD N, ZEGEYE H. Strong Convergence of an Implicit Iteration Process for a Finite Family of Generalized As- ymptotically Quasi-Nonexpansive Maps [J]. Comput Math Appl, 2007, 189(2): 1058-1065.
  • 9YILDIRM I, KHAN S H. Convergence Theorems for Common Fixed Points of Asymptotically Quasi-Nonexpansive Mappings in Convex Metric Spaces [J]. Comput Math Appl, 2012, 218(9): 4860-4866.
  • 10MA Z H, CHEN R D. Strong Convergence for a Finite Family of Generalized Asymptotocally Nonexpansive Mappings [J]. Physics Procedia, 2012, 33(5): 75-84.

引证文献4

二级引证文献8

西南大学学报（自然科学版）
2014年 第2期

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