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Hilbert空间中非伸展映像的不动点的粘滞迭代算法 被引量：2

The Viscosity Approximation Process for Nonspreading Mappings in Hilbert Spaces
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摘要 针对Hilbert空间中非伸展映像引入了一种新的粘滞迭代算法,获得了一个强收敛定理. In the present paper, the viscosity approximation process is studied and a strong convergence theorem is proved.
作者 周宇 刘元星 周海云
机构地区 军械工程学院基础部 河北经贸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24期222-226,共5页 Mathematics in Practice and Theory
基金 国家自然科学基金(11071053)
关键词 非伸展映像 粘滞迭代算法 强收敛 nonspreading mappings viscosity approximation process strong convergence theorem
分类号 O177.91 [理学—基础数学]
  • 相关文献

参考文献6

  • 1Kohsaka F and Takahashi W. Fixed point theorems for class of nonlinear mappings related to maximal monotone operators in Banach spaces[J]. Arch. Math., 2008, 91: 166-177.
  • 2Mainge P E. The viscosity approximation process for quasi-nonexpansive mappings in Hilbert spaces[J] C. M. A., 2010, 59: 74-79.
  • 3Agarwal R P, O'Regan Donal and Sahu D R. Fixed Point Theory for Lipschizian-Type Mappings with Applications[M]. Springer-Verlag, 2008.
  • 4Iemoto S, Takahashi W. Approximating common fixed points of nonexpansive mappings and nonspreading mappings in a Hilbert space[J]. Nonlinear Analysis: Theory, Methods & Applications, 2009, 71: 2082-2089.
  • 5Mainge P E. Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization[J]. Set-valued Anal., 2008, 16: 899-912.
  • 6张东凯,周海云.Hilbert空间中闭的拟非扩张映像不动点的另一迭代算法[J].河北师范大学学报（自然科学版）,2009,33(5):579-581. 被引量：7

二级参考文献6

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  • 2ALBER Y I ,REICH S. An Iterative Method for Solving a Class of Nonlinear Operator Equations in Banaeh Spaces [J]. Pan Amer Math J ,1994,4(3) :39-54.
  • 3BAUSCHKE H H, COMBETTES P L. A Weak-to-strong Convergence Principle for Fej6r-monotone Methods in Hilbert Spaces [J]. Math Oper Rese,2001,26(3) :248-264.
  • 4CHANG S S, CHO Y J, ZHOU Hai-yun. Iterative Methods for Nonlinear Operator Equations in Banach Spaces [ M], New York: Nova Science Publishers, 2002.
  • 5NAKAJO K, TAKAHASHI W. Strong Convergence Theorems for Nonexpansive Mappings and Nonexpansive Semigroups [ J ]. J Math Anal Appl,2003,279(6) :372-379.
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共引文献6

同被引文献11

  • 1Kohsaka F, Takahashi W. Fixed point theorems for class of nonlinear mappings related to maximal monotone operators in Banach spaces [J]. Arch. Math. 2008, 91: 166-177.
  • 2Takahashi W. Nonlinear Functional Analysis [M]. Yokohama Publishers, 2000.
  • 3Iemoto S, Takahashi W. Approximating common fixed points of nonexpansive mappings and non- spreading mappings in a Hilbert space [J]. Nonlinear Analysis: Theory, Methods and Applications, 2009, 71: 2082-2089.
  • 4Maing P E. Viscosity approximation process for qusi-nonexpansive mappings in Hilbert spaces [J]. Computers .Math ADD1. 2010. 59: 74-79.
  • 5AGARWAL R P, O' Regan Donal, SAHU D R. Fixed point theory for Lipschizian-type mappings with applications [M]. New York: Springer-Verlag, 2008: 1-375.
  • 6KOHSAKA F, TAKAHASHI W.Fixed point theorems for class of nonlinear mappings related to maximal monotone operators in Banach spaces[J]. Arch. Math., 2008,91 (2) : 166-177.
  • 7MAINGEP E. Strong convergence of projected suhgradient methods for nonsmooth and nonstrictly convex minimization [J]. Set-valued Anal., 2008,16(6) : 899- 912.
  • 8MAINGEP E. The viscosity approximation process forquasi-nonexpansive mappings in Hilbert spaces [J]. C. M. A., 2010,59(1):74-79.
  • 9IEMOTOS S, TAKAHASHI W. Approximating common fixed points of nonexpansive mappings and nonspreading mappings in a Hilbert space [J], Nonlinear Analysis: Theory, Methods & Applications, 2009,71 (3) :2082- 2089.
  • 10QIN X L. On the convergence of iterative processes for nonlinear operators [D]. Chinju; Gyeongsang National University, 2010.

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数学的实践与认识
2011年 第24期

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