不动点问题平衡问题及变分不等式问题的具弱压缩的粘性逼近

张石生; 李向荣; 陈志坚; 柳京爱

doi:10.3879/j.issn.1000-0887.2010.10.008

不动点问题平衡问题及变分不等式问题的具弱压缩的粘性逼近

doi: 10.3879/j.issn.1000-0887.2010.10.008

宜宾学院数学系,四川宜宾 644007;2.香港理工大学应用数学系,香港九龙;3.北京石油化工学院数理系,北京 102617

详细信息

作者简介:
张石生(1934- ),男,云南曲靖人,教授(联系人.E-mail:changss@yahoo.cn);陈志坚(E-mail:machanck@polyu.edu.hk);李向荣(E-mail:majlee@polyu.edu.hk);柳京爱(E-mail:liujingai@bipt.edu.cn)

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出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-09-08
- 刊出日期: 2010-10-15

Viscosity Approximation With Weak Contractions for Fixed Point Problem Equilibrium Problem and Variational Inequality Problem

Department of Mathematics, Yibin University, Yibin, Sichuan 644007, P. R. China;

摘要

摘要: 借助具弱压缩的粘性逼近，提出一种新的修正的迭代算法，用以寻求一公共元，它既是一无穷族非扩张映像的公共不动点集中的点，也是一有限族的平衡问题的解集中的点，而且它还是一变分不等式的解．在适当的条件下，一些强收敛定理在Hilbert空间的框架下被建立．所得结果推广和改进了Colao等,Plubtieng 等,Colao等,Yao等及其他人的一些最新的结果．
- 具弱压缩映像的粘性逼近 /
- 平衡问题 /
- 非扩张映像 /
- 隐迭代 /
- 极小化问题
Abstract: The purpose was by using the viscosity approximation method with a weak contraction to propose a modified iterative algorithm for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems which was also a solution of a variational inequality.Under suitable conditions,some strong convergence theorems were established in the framework of Hilbert spaces.The results presented improve and extend the corresponding results in Colao, et al [Nonlinear Anal,2009, 71:27082715], Plubtieng, et al [J Math Anal Appl,2007, 336:455-469],Colao, et al [J Math Anal Appl, 2008, 344:340-352],Yao, et al [Fixed Point Theory Appl,2007, Art ID64363] and others.
- viscosity approximation with weak contraction mapping /
- equilibrium problem /
- nonex-pansive mapping /
- implicititeration /
- minimization problem

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参考文献(12)

[1]	Browder F E, Petryshyn W V. Construction of fixed points of nonlinear mappings in Hilbert space[J]. J Math Anal Appl, 1967, 20: 197-228. doi: 10.1016/0022-247X(67)90085-6
[2]	Yamada I, Ogura N. Hybrid steepest descent method for the variational inequality problem over the fixed point set of certain-nonexpansive mappings[J]. Numer Funct Anal Optim, 2004, 25(7/8): 619-655.
[3]	Plubtieng S, Punpaeng R. A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces[J]. J Math Anal Appl, 2007, 336(1): 455-469. doi: 10.1016/j.jmaa.2007.02.044
[4]	Shimoji K,Takahashi W. Strong convergence to common fixed points of infinite nonexpansive mappings and applications[J]. Taiwanese J Math, 2001, 5(2): 387-404.
[5]	Colao V, Acedo G L, Marino G. An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings[J]. Nonlinear Anal,2009, 71(7/8): 2708-2715. doi: 10.1016/j.na.2009.01.115
[6]	Colao V, Marino G, Xu H K. An iterative method for finding common solutions of equilibrium problem and fixed point problems[J]. J Math Anal Appl, 2008, 344(1): 340-352. doi: 10.1016/j.jmaa.2008.02.041
[7]	Yao Y, Liou Y C, Yao J C. Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings[J]. Fixed Point Theory Appl, 2007, 2007.Art ID 64363.doi: 1155/2007/64363.
[8]	Alber Ya I, Guerre-Delabriere. Principles of weakly contractive maps in Hilbert spaces[C]Gohberg I,Lyubich Yu,Eds. New Results in Operator Theory and Its Applications,98.Basel: Birkhuser Verlag, 1997,7-22.
[9]	Song Y S. Equivalent theorems of the convergence between proximal type algorithms[J]. Nonlinear Anal, 2009, 71(1/2): 293-300. doi: 10.1016/j.na.2008.10.067
[10]	Rhoades B E. Some theorems on weakly contractive maps[J]. Nonlinear Anal, 2001, 47(4):2683-2693. doi: 10.1016/S0362-546X(01)00388-1
[11]	张石生.Banach空间中广义混合平衡问题[J]. 应用数学和力学, 2009, 30(9): 1033-1041.
[12]	Combettes P L, Hirstoaga S A.Equilibrium programming in Hilbert spaces[J]. J Nonlinear Convex Anal, 2005, 6(1): 2005: 117-136.

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不动点问题平衡问题及变分不等式问题的具弱压缩的粘性逼近

doi: 10.3879/j.issn.1000-0887.2010.10.008

作者简介:
张石生(1934- ),男,云南曲靖人,教授(联系人.E-mail:changss@yahoo.cn);陈志坚(E-mail:machanck@polyu.edu.hk);李向荣(E-mail:majlee@polyu.edu.hk);柳京爱(E-mail:liujingai@bipt.edu.cn)

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Viscosity Approximation With Weak Contractions for Fixed Point Problem Equilibrium Problem and Variational Inequality Problem

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不动点问题平衡问题及变分不等式问题的具弱压缩的粘性逼近

doi: 10.3879/j.issn.1000-0887.2010.10.008

作者简介: 张石生(1934- ),男,云南曲靖人,教授(联系人.E-mail:changss@yahoo.cn);陈志坚(E-mail:machanck@polyu.edu.hk);李向荣(E-mail:majlee@polyu.edu.hk);柳京爱(E-mail:liujingai@bipt.edu.cn)

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Viscosity Approximation With Weak Contractions for Fixed Point Problem Equilibrium Problem and Variational Inequality Problem

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作者简介:
张石生(1934- ),男,云南曲靖人,教授(联系人.E-mail:changss@yahoo.cn);陈志坚(E-mail:machanck@polyu.edu.hk);李向荣(E-mail:majlee@polyu.edu.hk);柳京爱(E-mail:liujingai@bipt.edu.cn)