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拟非扩张映像族的公共不动点的迭代方法 被引量：2

An Iterative Algorithm on Common Fixed Points for a Family of Quasi-Nonexpansive Mappings
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摘要 引入了修正的杂交投影迭代算法,用来构造Hilbert空间中拟非扩张映像族的公共不动点.使用新的算法证明了几个强收敛定理.新算法的优点是不要求映像具有次闭性质. In this paper, a modified hybrid projection iterative algorithms is introduced for constructing commn fixed points of a family of closed quasi-nonexpansive mappings in Hilbert spaces. With the modified iterative algorithm, several strong convergence theorems are proved. The main advantage of the new algorithms lies in the fact that the strong convergence results are obtained without making use of demi-closedness property for mappings considered here.
作者 张安 郭金题 周海云
机构地区 北京电子科技职业学院基础部 河北经贸大学数统学院 军械工程学院数学研究所 河北师范大学数学研究所
出处 《数学的实践与认识》 CSCD 北大核心 2010年第16期144-148,共5页 Mathematics in Practice and Theory
基金 国家自然科学基金(10771050)
关键词 拟非扩张映像族 闭映像 修正的杂交投影算法 HILBERT空间 强收敛 A family of quasi-nonexpansive mappings closed mapping modified hybrid projection algorithm Hilbert space strong convergence
分类号 O177.91 [理学—基础数学]
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参考文献12

  • 1Bauschke H H, Combettes P L. A weak-to-strong convergence principle for Fejer-monotone methods in Hilbert spaces[J]. Math Oper Rese, 2001, 26: 248-264.
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同被引文献19

  • 1谈斌.几类非线性算子零点或不动点迭代算法研究[D].石家庄:军械工程学院,2004.
  • 2Takahashi W. Nonlinear Functional Analysis [ M ]. Yokoha- ma: Yokohama Publishers, 2000.
  • 3ALBER Y I. Metric and generalizd projection operators in Banach spaces: properties and applications [ C ]//KARTSATOS A G. Theory and Applications of Nonlinear Operators of Accretive and Monotone Type [ M ]. New York: Marcel Dekker, 1996 : 15-50.
  • 4ALBER Y I, REICH S. An iterative method for solving a class of nonlinear operator equations in Banach spaces [ J ]. Pan Amer Math J. ,1994,4(3) :39-54.
  • 5BAUSCHKE H H, COMBETTES P L. A weak-to-strong convergence principle for Feje rmonotone methods in Hilbert space [J]. Math Oper. Rese., 2001,26(3) :248-264.
  • 6CHANG Shisheng, CHO Y J,ZHOU Haiyun. Iterative methods for nonlinear operator equations in Banach space [ M ]. New York : Nova Science Publishers, 2002.
  • 7NAKAJO K,TAKAHASHI W. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups [ J ]. J. Math Anal. Appl. , 2003,279(6) :372-379.
  • 8TAKAHASHI W. Nonlinear Functional Analysis [ M ]. Yokohama: Yokohama Publishers, 2000.
  • 9AOYAMA K, KOHSAKA F, WATARU T. Shring projection methods for fiemly nonexpansive mapping [ J ]. Nonliner Analysis, 2009 (10) : 1016-1023.
  • 10SONG Yisheng, CHEN Rudong. Strong convergence theorems on an iterative method for a family of finite nonex-pansive mappings[ J]. Applied Mathematics and Computation, 2006,180 (1) :275-287.

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数学的实践与认识
2010年 第16期

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