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Banach空间中非扩张映象不动点的黏性逼近 被引量：7

Viscosity Approximtion of Fixed Points for Nonexpansive Mappings in Banach Spaces
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摘要 设E是一致光滑的Banach空间,其范数是一致Gateaux可微的;设C是E之一非空闭凸子集,f:C→C是压缩映象,T:C→C是非扩张映象.本文用黏性逼近方法证明了在较一般的条件下,由(1.6)式定义的迭代序列{x_n)的强收敛性.本文推广和改进了一些近期结果. Let E be a uniformly smooth Banach space, whose norm is uniformly Gateaux differentiable. Let C be a closed convex subset of E, f ： C→C be a contractive mapping, and T ： C→C be a nonexpansive mapping. It is shown that under more general contractions of viscosity approximation methods, the sequence {xn} defined by （1.6） converges strongly. The results presented in this paper also extend and improve some recent results.
作者 赵良才 张石生
机构地区 宜宾学院数学系
出处 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2007年第4期919-924,共6页 数学研究与评论（英文版）
关键词 不动点 压缩映象 非扩张映象 黏性逼近 fixed point contractive mapping nonexpansive mapping viscosity approximation.
分类号 O177 [理学—基础数学]
  • 相关文献

参考文献15

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二级参考文献13

  • 1Chang S. S., Cho Y. J., Zhou H. Y., Iterative methods for nonlinear operator equations in Banach spaces,New York: Nova Science Publishers, Inc. 2002.
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共引文献4

同被引文献34

  • 1彭凤平,黄金平,戴敏.有限个λ半压缩映象族的强收敛定理[J].重庆师范大学学报（自然科学版）,2011,28(5):37-40. 被引量：1
  • 2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
  • 3张石生,杨莉,柳京爱.关于Banach空间非扩张半群的强收敛定理[J].应用数学和力学,2007,28(10):1146-1156. 被引量：7
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  • 5Yao Y H, Cho Y J, Liou Y C. Iterative algorithms for hierarchical fixed points problems and variational inequalities [ J ]. Math Comput Model,2010,52(9/10) :1697 -1705.
  • 6Moudafi A. Krasnoselski - Mann iteration for hierarchical fixed - point problems [ J ]. Inverse Problems ,2007,23 (4) : 1635 - 1675.
  • 7Maing P E, Moudafi A. Strong convergence of an iterative method for hierarchical fixed -point problems[ J ]. Pacific J Optim, 2007,3(3) :529 -538.
  • 8Solodov M. An explicit descent method for bilevel convex optimization [ J ]. J Convex Anal ,2007,14 (2) :227 -237.
  • 9Cianciaruso F, Marino G, Muglia L, et al. On a two - step algorithm for hierarchical fixed point problems and variational ine- qualities[J]. J Inequal Appl,2009,2009:208692.
  • 10Mainge P E. Approximation methods for common fixed points of non - expansive mappings in Hilbert paces [ J ]. J Math Anal Appl,2007,325 ( 1 ) :469 -479.

引证文献7

二级引证文献9

Journal of Mathematical Research and Exposition
2007年 第4期

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