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非扩张映射不动点的粘性逼近方法

Viscosity Approximation Methods for Fixed Point of Nonexpansive Mappings
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摘要 在具有一致Gateaux可微范数的Banach空间中,建立了一个改进的非扩张映射不动点的粘性逼近方法,并在一定条件下证明了该方法所得到的迭代序列的强收性.本文所得结果扩展并统一了部分文献的结果. Based on the viscosity iterative scheme,the modified iterative sequence for the fixed point of nonexpansive mappings has been established in a real Banach space with a uniformly Gateaux differentiable norm. Under some suitable conditions,we present the strong convergence of the iterative sequence. This method can extend and unify the results of some literature.
作者 唐艳
机构地区 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 2013年第6期267-271,共5页 Mathematics in Practice and Theory
基金 重庆市自然科学基金资助项目(CSTC 2012jjA00039)
关键词 非扩张映射 不动点 粘性逼近方法 强收敛 nonexpansive mappings fixed point viscosity approximation method strongconvergence
分类号 O177.91 [理学—基础数学]
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参考文献8

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  • 4唐艳,闻道君.Banach空间中渐近非扩张强连续半群不动点的粘性逼近[J].数学的实践与认识,2012,24(9):225-230. 被引量：2
  • 5闻道君,邓磊.渐近非扩张映射的粘滞逼近方法[J].西南师范大学学报（自然科学版）,2010,35(3):37-40. 被引量：7
  • 6Yao Yonghong. Strong convergence of an iterative method for nonexpansive mappings with control conditions[J]. Nonlinear Analysis, 2009, 70: 2332-2336.
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二级参考文献19

  • 1Xu H K. Viscosity Approximation Methods for Nonexpansive Mappings [J].J Math Anal Appl, 2004, 298:279 -,91.
  • 2Takahashi W. Non-linear Functional Analysis-Fixed Point Theory and its Applications [M]. Yokohama: Yokohama Publishers Ine, 2000.
  • 3Song Y. A New Sufficient Condition for the Strong Convergence of Halpern Type Iterations [J]. Appl Math Comput, 2008, 198:721-728.
  • 4Chang S S, Joseph Lee H W, Chan C K. On Reich's Strong Convergence Theorem for Asymptotically Nonexpansive Mappings in Banach Spaces [J].Nonlinear Anal, 2007, 66: 2364- 2374.
  • 5Yao Y, Chen R, Yao J C. Strong Convergence and Certain Conditions for Modified Mann Iteration [J']. Nonlinear Analysis, 2008, 68: 1687- 1693.
  • 6Xu H K. Iterative Algorithms for Non-linear Operators[J]. J Lond Math Soc, 2002, 66:240 - 256.
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  • 8Reich S. Strong convergence theorems for resolvents of accretive operators in Banach spaces[J]. J Math Anal Appl, 1980, 75: 287-292.
  • 9Chang 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.
  • 10Yonghong Yao. Strong convergence of an iterative method for nonexpansive mappings with control conditions[J]. Nonlinear Analysis, 2009, 70: 2332-2336.

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数学的实践与认识
2013年 第6期

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