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Banach空间中广义混合平衡问题

张石生

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. doi: 10.3879/j.issn.1000-0887.2009.09.004
引用本文: 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. doi: 10.3879/j.issn.1000-0887.2009.09.004
ZHANG Shi-sheng. On the Generalized Mixed Equilibrium Problem in Banach Spaces[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1033-1041. doi: 10.3879/j.issn.1000-0887.2009.09.004
Citation: ZHANG Shi-sheng. On the Generalized Mixed Equilibrium Problem in Banach Spaces[J]. Applied Mathematics and Mechanics, 2009, 30(9): 1033-1041. 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
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

On the Generalized Mixed Equilibrium Problem in Banach Spaces

  • 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.
  • [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
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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

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