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一类集值非线性混合变分包含问题的逼近解

张从军 孙敏

张从军, 孙敏. 一类集值非线性混合变分包含问题的逼近解[J]. 应用数学和力学, 2005, 26(9): 1121-1127.
引用本文: 张从军, 孙敏. 一类集值非线性混合变分包含问题的逼近解[J]. 应用数学和力学, 2005, 26(9): 1121-1127.
ZHANG Cong-jun, SUN Min. Approximate Solution to a Class of Multivalued Nonlinear Mixed Variational Inclusions[J]. Applied Mathematics and Mechanics, 2005, 26(9): 1121-1127.
Citation: ZHANG Cong-jun, SUN Min. Approximate Solution to a Class of Multivalued Nonlinear Mixed Variational Inclusions[J]. Applied Mathematics and Mechanics, 2005, 26(9): 1121-1127.

一类集值非线性混合变分包含问题的逼近解

基金项目: 国家自然科学基金资助项目(19871048);江苏省高校自然科学研究计划资助项目(04KJD110075)
详细信息
    作者简介:

    张从军(1956- ),男,教授,江苏省"333工程"培养对象,研究方向为非线性泛函分析及应用(联系人:Tel:+86-25-83494885;Fax:+86-25-84028410;E-mail:zcjyysxx@163.com).

  • 中图分类号: O177.91

Approximate Solution to a Class of Multivalued Nonlinear Mixed Variational Inclusions

  • 摘要: 在Hilbert空间中讨论了一类集值非线性混合变分包含问题逼近解的存在性,建立了变分包含问题与其预解方程的等价性,获得了3个迭代算法并研究了算法的收敛性.该结果推广统一了近期一些学者关于变分包含问题的相关结果.
  • [1] Muhammad Aslam Noor,Themistocles M Rassias. Resolvent equations for set-valued mixed variational inequalities[J].Nonlinear Analysis,2000,42,71—83. doi: 10.1016/S0362-546X(98)00332-0
    [2] Chang S S,Cho Y J,Lee B S,et al.Generalized set-valued variational inclusions in Banach spaces[J].Journal of Mathematical Analysis and Applications,2000,246,409—422. doi: 10.1006/jmaa.2000.6795
    [3] Chang S S.On the Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings[J].Compute Math Appl,1999,31(9):17—24.
    [4] 张从军.集值非线性混合变分包含问题解的存在性及其算法[J].应用数学学报,2005,28(1):65—72.
    [5] Lee C H,Ansari Q H,Yao J C.A perturbed algorithm for strongly nonlinear variational inclusions[J].Bull Austral Math Soc,2000,62,417—426. doi: 10.1017/S0004972700018931
    [6] DING Xie-ping.Perturbed proximal point algorithms for generalized quasi-variational inclusions[J].J Math Anal Appl,1997,210,88—101. doi: 10.1006/jmaa.1997.5370
    [7] Huang N J.Mann and Ishikawa type perturbed iterative algorithm for generalized nonlinear implicit quaip-variational inclusions[J].Com Math Appl,1998,35(10):1—7.
    [8] Khan M F,Ahman R,Ausari Q H.Generalized multivalued nonlinear variational inclusions monotone mappings[J].Adv Nonlinear Var Inequal,2000,3(1):93—101.
    [9] Chang S S.Existence and approximation of solutions to variational inclusions with accretive mappings in Banach spaces[J].Appl Math Mechanics,2001,22(9):898—904.
    [10] 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
    [11] ZHANG Cong-jun,Cho Y J,Wei S M.Variational inequalities and subjectivity for set-valued monotone mappings[J].Topological Methods in Nonlinear Analysis,1998,12(1):169—178.
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  • 被引次数: 0
出版历程
  • 收稿日期:  2003-05-26
  • 修回日期:  2005-04-05
  • 刊出日期:  2005-09-15

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