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非扩张映射粘性逼近的强收敛性 被引量：2

Strong Convergence of Viscosity Approximation for Nonexpansive Mappings
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摘要 在具有一致Gateaux可微范数的Banach空间中,研究了一个逼近非扩张映射不动点的粘性逼近方法,运用Banach极限推导了该逼近方法收敛的充分条件,并通过对该粘性逼近方法的修正逐步减少了收敛分析中的限制条件. In this paper, a viscosity approximation scheme is proposed for approximating the fixed point of nonexpansive mappings in a uniformly smooth Banach space, which sufficient condition for strong convergence is deduced with Banach limit. Restriction conditions of convergence are reduced successively based on the modified viscosity approximation method.
作者 王帮容 闻道君
机构地区 四川理工学院理学院 重庆工商大学数学与统计学院
出处 《数学的实践与认识》 CSCD 北大核心 2011年第12期216-221,共6页 Mathematics in Practice and Theory
基金 四川省人工智能重点实验室项目(2008RQ004)
关键词 非扩张映射 不动点 粘性逼近 BANACH极限 充分条件 nonexpansive mappings fixed point viscosity approximation method BanachIimit： suiTieient condition
分类号 O177.2 [理学—基础数学]
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参考文献10

  • 1Megginson R E. An Introduction to Banach Space Theory[M]. New York: Springer-Verlag, 1998.
  • 2Takahashi W, Ueda Y. On Reich's strong convergence theorems for resolvents of accretive opera- tors[J], J Math Anal Appl, 1984, 104: 546-553.
  • 3Zhou H Y, Wei L, Cho Y J. Strong convergence theorems on an iterative method for a family of finite nonexpansive mappings in reflexive Banach spaces[J], Appl Math Comput, 2006, 173: 196-212.
  • 4Chang S S. On Chidume's open questions and approximation solutions of multivalued strongly accretive mappings equations in Banach spaces[J], J Math Anal Appl, 1997, 216: 94-111.
  • 5Yao Y, Chen R, Yao J C. Strong convergence and certain conditions for modified Mann iteration[J]. Nonlinear Analysis, 2008, 68: 1687-1693.
  • 6Song Y. A new sufficient condition for the strong convergence of Halpern type iterations[J], Appl Math Comput, 2008, 198: 721-728.
  • 7Suzuki T. Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter non- expansive semigroups without Dochner integrals[J], J Math Anal Appl, 2005, 305: 227-239.
  • 8Xu H K. It'erative algorithms for non-linear operators[C], J Lond Math Soc, 2002, 66: 240-256.
  • 9闻道君,邓磊.一般变分不等式的三步迭代算法[J].四川师范大学学报（自然科学版）,2009,32(4):436-438. 被引量：12
  • 10闻道君.混合拟变分不等式的预测-校正算法[J].西南师范大学学报（自然科学版）,2009,34(5):41-44. 被引量：8

二级参考文献15

  • 1方长杰,郑莲,丁协平.解广义混合似变分不等式的预测校正迭代算法[J].四川师范大学学报（自然科学版）,2005,28(1):10-14. 被引量：9
  • 2刘小兰,何诣然.非连续的广义拟变分不等式问题的存在性定理[J].四川师范大学学报（自然科学版）,2007,30(1):22-26. 被引量：4
  • 3倪如俊,邓磊.完全广义混合隐拟似变分包含问题解的预测-矫正算法[J].西南大学学报（自然科学版）,2007,29(2):22-26. 被引量：9
  • 4Tseng P. Further Applications of a Splitting Algorithm to Decomposition in Variational Inequalities and Convex Programming[J].Math Prog, 1990, 48:249--264.
  • 5Marcotte P, Wu J H. On The Convergence of Projection Methods:Application to the Decomposition of Affine Variational Inequalities [J].J Optim Theory Appl, 1995, 85:347 --362.
  • 6Zhu D L, Marcotte P. Co-coercivity and Its Role in the Convergence of Iterative Schemes for Solving Variational Inequalities[J].SIAM J Optim, 1996, 6(3) : 714 - 726.
  • 7Facehinei F, Pang J S. Finite-dimensional Variational Inequality and Complementarity Problems 1 and 2 [M]. New York: Springer-Verlag, 2003.
  • 8Yang Q. On Variable-step Relaxed Projection Algorithm for Variational Inequalities[J].J Math Anal Appl, 2005, 302:166 -- 179.
  • 9Yang Q. The Revisit of a Projection Algorithm with Variable Steps for Variational Inequalities[J]. J Ind Manage Optim, 2005, 1(2): 211--217.
  • 10Zhao Jin-ling, Yang Qing-zhi. Weak Co-coercivity and Its Applications in Several Algorithms for Solving Variational Inequalities [J].Appl MathComput, 2008, 201: 200--209.

共引文献12

同被引文献10

  • 1张石生.Banach空间中非扩张映象的黏性逼近方法[J].数学学报（中文版）,2007,50(3):485-492. 被引量：13
  • 2Browder F E. Convergence of approximates to fixed points of nonexpansive nonlinear mappings in Banach spaces[J]. Arch Ration Mech Anal, 1967, 24: 82-90.
  • 3Reich S. Strong convergence theorems for resolvents of accretive operators in Banach spaces[J]. J Math Anal Appl, 1980, 75: 287-292.
  • 4Chang S S. On Chidume's open questions andapproximation solutions of multivalued strongly ac- cretive mappings equations in Banach spaces[J]. J Math Anal Appl, 1997, 216:94 -111.
  • 5Yonghong Yao. Strong convergence of an iterative method for nonexpansive mappings with control conditions[J]. Nonlinear Analysis, 2009, 70: 2332-2336.
  • 6S Reich. On the Aymptotic behavior of nonlinear semigroups and the range of accretive operators[J]. J Math Anal Appl, 1981, 79: 113-126.
  • 7Liu L S. Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach space[J]. J Math Anal Appl, 1995, 194: 114-125.
  • 8田有先,陈六新.有限一致拟-李卜希兹映象族公共不动点的逼近[J].西南大学学报（自然科学版）,2009,31(4):25-29. 被引量：6
  • 9唐艳,闻道君.非扩张映射不动点的粘性逼近方法[J].重庆工商大学学报（自然科学版）,2009,26(5):420-423. 被引量：2
  • 10高兴慧,马乐荣,周海云.拟φ—非扩张映像族的公共不动点的强收敛定理[J].数学的实践与认识,2011,41(20):233-239. 被引量：1

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数学的实践与认识
2011年 第12期

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