Hilbert空间中关于广义平衡问题与不动点问题公共解的收敛定理(英文)

Convergence Theorems of Common Elements for Generalized Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

下载PDF

导出

摘要本文在Hilbert空间中引进了一迭代方法来逼近两个集合的公共元素,这两个集合分别是一类广义平衡问题的解集和两个渐近非扩张映射公共不动点集.得到一强收敛定理,所得结果提高和推广了许多作者的相应结果. We introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of two asymptotically nonexpansive mappings in Hilbert spaces and then obtain a strong convergence theorem.Our results improve and extend the corresponding results announced by many others.

作者刘英

机构地区河北大学数学与计算机学院

出处《应用数学》 CSCD 北大核心 2011年第4期738-745,共8页 Mathematica Applicata

基金 the Natural Science Youth Foundation of Hebei Province(A2011201053, A2010000191) the Natural Science Youth Foundation of Hebei Education Commission(2010110)

关键词度量投影不动点广义平衡问题渐近非扩张映射逆强单调映射 Metric projection Fixed point Generalized equilibrium problem Asymptotically nonexpansive mapping Inverse-strongly monotone mapping

分类号 O177.91 [理学—基础数学]

引文网络
相关文献

参考文献11

1Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems [J]. Math. Stud. ,1994,63:123-145.
2LIU Ying. Ageneral iterative method for equilibrium problems and strict pseudo-contractions in Hilbert spaces[J]. Nonlinear Anal. , 2009,71 : 4852-4861.
3Tada A,Takahashi W. Strong convergence theorem for an equilibrium problem and a nonexpansive map- ping[J]. J. Optim. Theory Appl. , 2007,133 : 359-370.
4Takahashi S, Takahashi W. Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaees[J]. J. Math. Anal. Appl. , 2007,331 : 506-515.
5Takahashi W, Toyoda M. Weak convergence theorems for nonexpansive mappings and monotone map- pings[J]. J. Optim. Theory Appl. ,2003 ,118:417-428:.
6CHEN Junmin,ZHANG Lijuan,FAN Tiegang. Viscosity approximation methods for nonexpansive map- pings and monotone mappings[J]. J. Math. Anal. Appl. , 2007,334: 1450-1461.
7Iiduka H,Takahashi W. Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings[J]. Nonlinear Anal. , 2005,61 : 341-350.
8Takahashi S,Takahashi W. Strong convergence theorems for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space[J]. Nonlinear Analysis,2008,69..1025-1033.
9Plubtieng S,Ungchittrakool K. Strong convergence of modified Ishikawa iteration for two asymptotically nonexpansive mappings and semigroups[J]. Nonlinear Analysis, 2007,67 : 2306-2315.
10Goebel K,Kirk W A. A fixed point theorem for asymptotically nonexpansive mappings[J]. Proc. Amer. Math. Soc., 1972,35:171-174.

1秦秀根,黄建华.广义均衡问题和非扩张映射的强收敛定理[J].福州大学学报（自然科学版）,2012,40(3):285-292.
2张丽娟,佟慧.不动点集和零点集公共元的强弱收敛性[J].数学学报（中文版）,2015,58(4):601-612.
3吴艳秋,夏福全.Hilbert空间中变分不等式组的两步投影算法[J].四川师范大学学报（自然科学版）,2011,34(5):615-620. 被引量：2
4王桂祥,李友明.模糊γ-度强单调映射的变分不等式[J].东北电力学院学报,2001,21(2):17-20.
5史沧红,吴定平.非扩张映射族和单调映射迭代算法的收敛性[J].成都信息工程学院学报,2013,28(1):72-77.
6唐艳.一族强单调映射的公共零点的强收敛定理[J].重庆工商大学学报（自然科学版）,2013,30(3):13-16. 被引量：1
7朱新霞,黄胜利.一类非扩张型映射的不动点与变分包含问题的公共解[J].贵州大学学报（自然科学版）,2008,25(1):9-13.
8游贤焕,黄建华,秦秀根.广义均衡组和非扩张映射映像不动点公共元的强收敛定理[J].福州大学学报（自然科学版）,2014,42(2):167-172.
9田明,邓斌超.均衡、不动点及变分包含问题公共解的算法[J].中国民航大学学报,2010,28(5):55-59.
10刘英,陈永利.Banach空间中3类问题公共解的弱收敛定理[J].数学年刊（A辑）,2009,30(3):345-352.

应用数学

2011年第4期

浏览历史

内容加载中请稍等...

Hilbert空间中关于广义平衡问题与不动点问题公共解的收敛定理(英文)

参考文献11

相关作者

相关机构

相关主题

浏览历史