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

张德金, 向淑文, 邓喜才, 杨彦龙

系统科学与数学 ›› 2021, Vol. 41 ›› Issue (1) : 115-125.

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PDF(422 KB)
系统科学与数学 ›› 2021, Vol. 41 ›› Issue (1) : 115-125. DOI: 10.12341/jssms14099
论文

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

    张德金1,2,向淑文1,邓喜才3,杨彦龙1
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Generic Stability of the Set of Solutions for Vector-Valued Quasi-Variational Inequality Under Constraint Graph Topology

    ZHANG Dejin1,2 ,XIANG Shuwen1 ,DENG Xicai3 ,YANG Yanlong1
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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.}

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 vector-valued 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.

关键词

向量值拟变分不等式 / 图像拓扑 / / 通有稳定性.

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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. 系统科学与数学, 2021, 41(1): 115-125. https://doi.org/10.12341/jssms14099
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. Journal of Systems Science and Mathematical Sciences, 2021, 41(1): 115-125 https://doi.org/10.12341/jssms14099
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