| 反Banach空间内涉及广义混合似臣分不等式问题的双水平广义混合平衡问题 |
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| 引用本文： | 丁协平. 反Banach空间内涉及广义混合似臣分不等式问题的双水平广义混合平衡问题[J]. 应用数学和力学, 2011, 32(11) |
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| 作者姓名： | 丁协平 |
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| 作者单位： | 四川师范大学数学与软件科学学院,成都,610068 |
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| 基金项目： | 四川省重点学科建设基金资助项目(SZD0406); 四川师范大学重点科研基金(09ZDL04) |
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| 摘 要： | 在自反Banach空间内,引入和研究了一类新的涉及广义混合似变分不等式问题的双水平广义混合平衡问题(BGMEP).首先,为了计算BGMEP的近似解,引入了一类辅助广义混合平衡问题(AGMEP).由使用一极小极大不等式,在没有任何强制条件的相当温和假设下,证明了AGMEP解的存在性和唯一性.利用辅助原理技巧,建议和分析了一类计算BGMEP的近似解的新迭代算法.在没有任何强制条件的相当温和假设下,证明了由算法生成的迭代序列的强收敛性.这些结果是新的并且推广了这一领域内某些最近结果.
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| 关 键 词： | 广义混合似变分不等式 双水平广义混合平衡问题 辅助原理 迭代算法 自反Banach空间 |
Bilevel Generalized Mixed Equilibrium Problems Involving Generalized Mixed Variational-Like Inequality Problems in Reflexive Banach Spaces |
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| DING Xie-ping. Bilevel Generalized Mixed Equilibrium Problems Involving Generalized Mixed Variational-Like Inequality Problems in Reflexive Banach Spaces[J]. Applied Mathematics and Mechanics, 2011, 32(11) |
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| Authors: | DING Xie-ping |
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| Affiliation: | DING Xie-ping (College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610068,P.R.China) |
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| Abstract: | A new class of bilevel generalized mixed equilibrium problems(BGMEP) involving generalized mixed variational-like inequality problems was introduced and studied in reflexive Banach spaces.First,an auxiliary generalized mixed equilibrium problem(AGMEP) to compute the approximate solutions of the bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems was introduced.By using a minimax inequality,the existence and uniqueness of solutions of the AGMEP was ... |
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| Keywords: | generalized mixed equilibrium problem involving generalized mixed variational-like inequality problem auxiliary principle iterative algorithm reflexive Banach space |
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