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非扩张映象和逆-强单调映象关于扰动集合的稳定性 被引量：2

On the stability of nonexpansive mappings and inverse-strong monotonic mappings with perturbed constraint sets
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摘要 在H ilbert空间中研究迭代序列逼近非扩张自映象S:Ω|→Ω的不动点和逆-强单调算子T:Ω|→H的变分不等式解.当闭凸紧集Ω、非扩张映象S、逆-强单调算子T、度量投影算子PΩ的扰动满足适当的条件时,扰动迭代序列的强收敛性仍然成立.所得结果推广了近期一些相应的结果. It was studied iterative approximations for finding a common element of fixed points of a nonexpansire mapping and set of solutions of the variational inequalities for an inverse-strong monotonic mappings in Hilbert space. The conditons which guarantee strong convergence and stability of these approximations with respect to perturbations of constraint set .Ω, nonexpansive operator S, metric projection operator Pa were considered. It was showed that the sequence strongly converges to a common element of two sets.
作者 徐卫 王元恒 张涛
机构地区 浙江师范大学数理与信息工程学院 中国人民武装警察部队上海政治学院数理教研室
出处 《浙江师范大学学报（自然科学版）》 CAS 2007年第4期399-405,共7页 Journal of Zhejiang Normal University:Natural Sciences
基金 国家自然科学基金资助项目(10561007)
关键词 不动点 变分不等式的解 度量投影 HAUSDORFF距离 扰动迭代序列 fixed point solution of variational inequality metric projection Hausdorff distance perturbation of iterative sequence
分类号 O177.91 [理学—基础数学]
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参考文献18

  • 1Browder F E.Nonlinear monotone operators and convex sets in Banach spaces[J].Bull Amer Math Soc,1965,71:780-785.
  • 2Browder F E.The fixed point theory of multi-valued mappings in topoligical vector spaces[J].Math Ann,1968,177(4):281-301.
  • 3Bruck R E.On the weak convergence of an ergodic iteration for the solutions of variational inequalities for monotone operators in Hilbert space[J].J Math Anal Appl,1977,61:159-164.
  • 4Browder F E,P etryshyn W V.Constraction of fixed points of nonlinear mappings in Hilbert spaces[J].J Math Anal Appl,1967,20:197-228.
  • 5Iiduka H,Takahashi W,Toyoda M.Approximation of solutions of variational inequalities for monotone mappings[J].PanAmer Math J,2004,14:49-61.
  • 6Liu Fengshan,Nashed M Z.Regularization of nonlinear ill-posed variational inequalities and convergence rates[J].Set-Valued Anal,1998,6(4):313-344.
  • 7Nakajo K,Takahashi W.Strong and weak convergence theorems by an improved splitting method[J].J Comm Appl Nonlinear Anal,2002,9:99-107.
  • 8Takahashi W.Nonlinear variational inequities and fixed point theorems[J].J Math Soc Japan,1976,28:168-187.
  • 9Takahashi W.Convex Analysis and Approximation of Fixed Points[M].Yokohama:Yokohama Publishers,2000.
  • 10Takahashi W.Nonlinear Functional Analysis[M].Yokohama:Yokohama Publishers,2000.

同被引文献16

  • 1黄建锋,王元恒.关于一种严格伪压缩映象Mann迭代序列的强收敛性[J].浙江师范大学学报（自然科学版）,2006,29(4):378-381. 被引量：4
  • 2姚永红,陈汝栋,周海云.非扩张映象不动点的迭代算法[J].数学学报（中文版）,2007,50(1):139-144. 被引量：6
  • 3Xu Hongkun. Viscosity approximation methods for nonexpansive mappings[J]. J Math Anal Appl,2004,298 ( 1 ) :279-291.
  • 4DeimLiwg K. Zeros of accretive operators[J]. Manuscripta Mathematica, 1974,13 (4) :365-374.
  • 5Takahashi W, Ueda Y. On Reich's strong convergence theorems for resolvents of accretive operators[J]. J Math Anal Appl, 1984,104 (2) :546-553.
  • 6Song Yisheng. Chen Rudong. Convergence theorems of iterative algorithms for continuous pseudneontraetive mappings[ J ]. Nonlinear Analysis 2007,67 ( 2 ) :486-497.
  • 7Megginson R E. An Introduction to Banach Space Theory[M]. New York:Springer-Verlag, 1998.
  • 8Halpern B. Fixed points of nonexpanding maps[ J]. Bull Amer Math Soc, 1967,73:957-961.
  • 9Lions P L. Approximation de points fixes de constractions [ J ]. CRAcad Sci Paris Ser A, 1977,284 ( 21 ) : 1357-1359.
  • 10Wittmann R. Approximation of fixed points of nonexpansive mappings[ J]. Arch Math, 1992,58 (5) :486-491.

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浙江师范大学学报（自然科学版）
2007年 第4期

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