| 约束图像拓扑下的向量值拟变分不等式解集的通有稳定性 |
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| 引用本文： | 张德金,向淑文,邓喜才,杨彦龙.约束图像拓扑下的向量值拟变分不等式解集的通有稳定性[J].系统科学与数学,2021(1):115-125. |
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| 作者姓名： | 张德金 向淑文 邓喜才 杨彦龙 |
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| 作者单位： | 贵州大学数学与统计学院;贵州师范大学数学科学学院;贵州师范学院数学与计算机科学学院 |
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| 基金项目： | 国家自然科学基金(11861025,11761023,71961003,11561013);教育部博士点基金(20115201110002);贵州省科技计划项目(黔科合平台人才[2018]5769号,[2017]5788号和黔科合LH字[2017]7223号);贵州省普通高等学院科技拔尖人才支持计划黔教合KY字([2017]81);贵大人基合字[2019]49资助课题。 |
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| 摘 要： | 主要运用研究通有性质的方法研究向量值拟变分不等式解的稳定性.首先引入约束映射在图像拓扑意义下的Hausdorff度量,这是一种有别于通常一致度量的新度量,然后在此弱图像拓扑下,给出并证明了关于向量值拟变分不等式解的通有稳定性的几个结论.结论表明,在Baire分类的意义下,大多数的向量值拟变分不等式问题的解关于新定义的度量都是本质的.
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| 关 键 词： | 向量值拟变分不等式 图像拓扑 解 通有稳定性 |
Generic Stability of the Set of Solutions for Vector-Valued Quasi-Variational Inequality Under Constraint Graph Topology |
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| ZHANG Dejin,XIANG Shuwen,DENG Xicai,YANG Yanlong.Generic Stability of the Set of Solutions for Vector-Valued Quasi-Variational Inequality Under Constraint Graph Topology[J].Journal of Systems Science and Mathematical Sciences,2021(1):115-125. |
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| Authors: | ZHANG Dejin XIANG Shuwen DENG Xicai YANG Yanlong |
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| Institution: | (School of Mathematics and Statistics,Guizhou University,Guinyang 550025;School ofMathematical Sciences,Guizhou Normal University,Guiyang 550025;School of Mathematics and Computer Science,Guizhou Normal College,Guiang 550018) |
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| Abstract: | In this paper,the stability of solutions of vector-valued quasi-variational inequalities is studied by means of the research methods of generic properties.First,the Hausdorff metric of constrain correspondence under the sense of graph topology is introduced,which is a new metric different from the usual uniform metric,and then we study and obtain the results of generic stability of the solutions of vectorvalued quasi-variational inequalities under this weaker graph topology.It is shown that most of the solutions of vector-valued quasi-variational inequality problems are essential with respect to this new metric in the sense of Baire category. |
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| Keywords: | Vector-valued quasi-variational inequality graph topology solutions generic stability |
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