Banach空间中广义混合平衡问题

张石生

doi:10.3879/j.issn.1000-0887.2009.09.004

Banach空间中广义混合平衡问题

doi: 10.3879/j.issn.1000-0887.2009.09.004

张石生

宜宾学院数学系,四川宜宾 644007

详细信息

作者简介:
张石生(1934- ),男,云南省曲靖市人,教授(E-mail:changss@yahoo.cn).

中图分类号: O177.91
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- 被引次数: 0
出版历程
- 收稿日期: 2009-04-04
- 修回日期: 2009-07-24
- 刊出日期: 2009-09-15

On the Generalized Mixed Equilibrium Problem in Banach Spaces

ZHANG Shi-sheng

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

摘要

摘要: 在一致光滑和严格凸的Banach空间的框架下，采用综合性算法，借以寻求广义混合平衡问题的解集、变分不等式的解集、及一有限族的拟-非扩张映象公共不动点集的公共元．作为应用，把所得结果应用于研究最优化问题．所得结果推广和改进了Ceng,Takahashi,Qin等人所发布的新结果．
- 广义混合平衡问题 /
- 混合平衡问题：平衡问题 /
- 变分不等式 /
- 拟-非扩张映象 /
- 极大单调映象 /
- 单调映象
Abstract: The purpose is by using hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem,the set of solutions for variational inequality problem and the set of common fixed points for a finite family of quasi-Φ-nonexpansive mappings in a uniformly smooth and strictly convex Banach space.By utilizing the results for the study of optimization problem,it shows that the results improve and extend the corresponding results announced recently by many others such as Ceng,Takahashi,Qin,et al.
- generalized mixed equilibrium problem /
- mixed equilibrium problem /
- equilibrium problem /
- variational inequality /
- quasi-Φ- nonexpansive mapping /
- maximal monotone operator

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参考文献(12)

[1]	CENG Lu-chuan,YAO Jen-chih.A hybrid iterative scheme for mixed equilibrium problems and fixed point problems[J].J Comput Appl Math,2008,214(1):186-201. doi: 10.1016/j.cam.2007.02.022
[2]	Browder F E.Existence and approximation of solutions of nonlinear variational inequalities[J].Proc Natl Acad Sci USA,1966,56(4):1080-1086. doi: 10.1073/pnas.56.4.1080
[3]	Takahashi W,Zembayashi K.Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces[J].Nonlinear Anal,2009,70(1):45-57. doi: 10.1016/j.na.2007.11.031
[4]	Takahashi S,Takahashi W.Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces[J].J Math Anal Appl,2007,331(1):506-515. doi: 10.1016/j.jmaa.2006.08.036
[5]	Qin X L,Shang M,Su Y.A general iterative method for equilibrium problem and fixed point problems in Hilbert spaces[J].Nonlinear Anal,2008,69(11):3897-3909. doi: 10.1016/j.na.2007.10.025
[6]	Cioranescu I.Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems[M].Dordrecht:Kluwer,1990.
[7]	Alber Y I.Metric and generalized projection operators in Banach spaces: properties and applications[A].In: Kartosator A G,Ed.Theory and Applications of Nonlinear Operators of Accretive and Monotone Type[C].New York:Marcel Dekker,1996,15-50.
[8]	Kamimura S,Takahashi W.Strong convergence of a proximal-type algorithm in a Banach space[J].SIAM J Optim,2002,13(3):938-945. doi: 10.1137/S105262340139611X
[9]	Matsushita S,Takahashi W.Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces[J].Fixed Point Theory Appl,2004,2004(1):37-47.
[10]	Nilsrakoo W,Saejung S.Strong convergence to common fixed points of countable relatively quasi-nonexpansive mappings[J].Fixed Point Theory Appl,2008,2008：Article ID 312454,doi: 10.1155/2008/312454.
[11]	Blum E,Oettli W.From optimization and variational inequalities to equilibrium problems[J].Math Studient,1994,63(1/4):123-145.
[12]	Xu H K.Inequalities in Banach spaces with applications[J].Nonlinear Anal,1991,16(2):1127-1138. doi: 10.1016/0362-546X(91)90200-K