留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

拟变分包含及不动点问题公解的算法

张石生 李向荣 陈志坚

张石生, 李向荣, 陈志坚. 拟变分包含及不动点问题公解的算法[J]. 应用数学和力学, 2008, 29(5): 515-524.
引用本文: 张石生, 李向荣, 陈志坚. 拟变分包含及不动点问题公解的算法[J]. 应用数学和力学, 2008, 29(5): 515-524.
ZHANG Shi-sheng, LEE Joseph H W, CHAN Chi Kin. Algorithms of Common Solutions for Quasi Variational Inclusion and Fixed Point Problems[J]. Applied Mathematics and Mechanics, 2008, 29(5): 515-524.
Citation: ZHANG Shi-sheng, LEE Joseph H W, CHAN Chi Kin. Algorithms of Common Solutions for Quasi Variational Inclusion and Fixed Point Problems[J]. Applied Mathematics and Mechanics, 2008, 29(5): 515-524.

拟变分包含及不动点问题公解的算法

详细信息
    作者简介:

    张石生(1934- ),男,云南曲靖人,教授(联系人.Tel:+86-28-85415930;E-mail:sszhang_1@yahoo.com.cn).

  • 中图分类号: O177.91

Algorithms of Common Solutions for Quasi Variational Inclusion and Fixed Point Problems

  • 摘要: 介绍了一种新的迭代算法,在Hilbert空间的框架下,用以寻求具多值极大单调映象和逆-强单调映象的变分包含的解集与非扩张映象的不动点集的公共元.在适当的条件下,逼近于这一公共元的某些强收敛定理被证明.所得结果是新的,它不仅改进和推广了Korpelevich 的结果,而且也推广和改进了Iiduka和Takahashi,Takahashi和Toyoda,Nadezhkina和Takahashi及Zeng和Yao等人的最新结果.
  • [1] Noor M A,Ames K W I F.Sensitivity analysis for quasi variational inclusions[J].J Math Anal Appl,1999,236(2):290-299. doi: 10.1006/jmaa.1999.6424
    [2] Chang S S.Set-valued variational inclusions in Banach spaces[J].J Math Anal Appl,2000,248:438-454. doi: 10.1006/jmaa.2000.6919
    [3] Chang S S.Existence and approximation of solutions of set-valued variational inclusions in Banach spaces[J].Nonlinear Anal,TMA,2001,47(1):583-594. doi: 10.1016/S0362-546X(01)00203-6
    [4] Demyanov V F,Stavroulakis G E,Polyakova L N,et al.Quasidifferentiability and Nonsmooth Modeling in Mechanics,Engineering and Economics[M].Dordrecht:Kluwer Academic,1996.
    [5] Noor M A.Generalized set-valued variational inclusions and resulvent equations[J].J Math Anal Appl,1998,228(1):206-220. doi: 10.1006/jmaa.1998.6127
    [6] Browder F E.Nonlinear monotone operators and convex sets in Banach spaces[J].Bull Amer Math Soc,1965,71(5):780-785. doi: 10.1090/S0002-9904-1965-11391-X
    [7] Hartman P,Stampacchia G.On some nonlinear elliptic differential equations[J].Acta Math,1966,115(1):271-310. doi: 10.1007/BF02392210
    [8] Lions J L,Stampacchia G.Variational inequalities[J].Comm Pure Appl Math,1967,20:493-517. doi: 10.1002/cpa.3160200302
    [9] Browder F E,Petryshyn W V.Construction of fixed points of nonlinear mappings in Hilbert spaces[J].J Math Anal Appl,1967,20:197-228. doi: 10.1016/0022-247X(67)90085-6
    [10] Iiduka H,Takahashi W,Toyoda M.Approximation of solutions of variational inequalities for monotone mappings[J].Pan Amer Math J,2004,14:49-61.
    [11] Liu F,Nashed M Z.Regularization of nonlinear ill-posed variational inequalities and convergence rates[J].Set-Valued Analysis,1998,6(4):313-344. doi: 10.1023/A:1008643727926
    [12] Takahashi W,Toyoda M.Weak convergence theorems for nonexpansive mappings and monotone mappings[J].J Optim Theory Appl,2003,118(2):417-428. doi: 10.1023/A:1025407607560
    [13] Iiduka H,Takahashi L W.Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings[J].Nonlinear Anal,TMA,2005,61(3):341-350. doi: 10.1016/j.na.2003.07.023
    [14] Korpelevi[KG-*4]. cˇ G M.An extragradient method for finding saddle points and for other problems[J].Ekonomika i Matematicheskie Metody,1976,12(4):747-756.
    [15] Nadezhkina N,Takahashi W.Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings[J].J Optim Theory Appl,2006,128(1):191-201. doi: 10.1007/s10957-005-7564-z
    [16] Zeng L C,Yao J C.Strong convergence theorem by an extragradient method for fixed point problems and variational inequality problems[J].Taiwanese Journal of Mathematics,2006,10(5):1293-1303.
    [17] Brezis H.Opérateur Maximaux Monotones et Semiproupes de Contractions Dans les Espaces de Hilbert[M].Amsterdam:North-Holland,1973.
    [18] Pascali Dan.Nonlinear Mappings of Monotone Type[M].Amsterdam,Netherlands:Sijthoff and Noordhoff International Publishers,1978.
    [19] Liu L S.Ishikawa and Manniterative processes with errors for nonlinear strongly accretive mappings in Banach spaces[J].J Math Anal Appl,1995,194(1):114-125. doi: 10.1006/jmaa.1995.1289
    [20] Goebel K,Kirk W A.Topics in metric fixed point theory[A].In:Cambridge Studies in Advanced Mathematics[C].28.London:Cambridge University Press,1990.
    [21] Bruck R E.On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert spaces[J].J Math Anal Appl,1977,61:159-164. doi: 10.1016/0022-247X(77)90152-4
    [22] Chang S S.Some problems and results in the study of nonlinear analysis[J].Nonlinear Anal,TMA,1997,30(7):4197-4208. doi: 10.1016/S0362-546X(97)00388-X
  • 加载中
计量
  • 文章访问数:  2951
  • HTML全文浏览量:  136
  • PDF下载量:  840
  • 被引次数: 0
出版历程
  • 收稿日期:  2007-08-30
  • 修回日期:  2008-03-19
  • 刊出日期:  2008-05-15

目录

    /

    返回文章
    返回