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
Generic Stability of the Set of Solutions for Vector-Valued Quasi-Variational Inequality Under Constraint Graph Topology
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.}
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.
向量值拟变分不等式 / 图像拓扑 / 解 / 通有稳定性. {{custom_keyword}} /
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