Mordukhovich导数的一些性质及其在Banach空间局部变分不等式中的应用
Some Properties of Mordukhovich Derivatives with Applications to Locally Variational Inequalities in Banach Spaces
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中文总结 AI 辅助
本文研究Banach空间中Frechet导数与Mordukhovich导数的联系，发现集值映射导数性质，引入局部变分不等式概念，并揭示其解与Mordukhovich导数的关联。
中文摘要 AI 辅助
本文研究Banach空间中单值映射的Frechet导数与Mordukhovich导数之间的联系。我们将发现集值映射的Mordukhovich导数的一些性质，并通过有限维Banach空间中的集值度量投影算子加以说明。我们引入Banach空间中局部变分不等式的概念，该概念关注在特定邻域内而非整个全局域中寻找解；并发现局部变分不等式问题的解与Mordukhovich导数之间的联系。
英文摘要
In this paper, we will investigate the connection between Frechet derivatives and Mordukhovich derivatives of single-valued mappings in Banach spaces. We will find some properties of Mordukhovich derivatives of set-valued mappings, which will be demonstrated by the set-valued metric projection operator in finite dimensional Banach spaces. We introduce the concept of locally variational inequalities in Banach spaces, which focus on finding solutions within some specific neighborhoods rather than across the entire global domain; and we find the connection between the solutions of locally variational inequality problems and the Mordukhovich derivatives.
发表机构
- Shawnee State University（肖尼州立大学）
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