一般巴拿赫空间中集值度量投影的Mordukhovich导数与覆盖常数
Mordukhovich Derivatives and Covering Constant for Set-Valued Metric Projection in General Banach Spaces
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中文总结 AI 辅助
本文得到l₁空间到其单位闭球的集值度量投影算子的显式表示，研究其Mordukhovich导数性质以计算覆盖常数，还针对二维巴拿赫空间得到该投影算子的显式解并详细计算其导数。
中文摘要 AI 辅助
本文中，我们得到从l₁空间到其单位闭球的集值度量投影算子的显式表示。利用该表示，我们研究了该集值度量投影算子的Mordukhovich导数的性质，这些性质被用于计算其覆盖常数。作为特例，我们考虑二维巴拿赫空间，得到从所考虑的二维巴拿赫空间到其单位闭球的集值度量投影算子的显式解，并借助这些解详细计算其Mordukhovich导数。
英文摘要
In this paper, we find the explicit representation of the set-valued metric projection operator from l1 to the unit closed ball in l1. By using this representation, we investigate the properties of the Mordukhovich derivatives of the set-valued metric projection operator, which is applied to calculate its covering constant. As a special case, we consider the 2-d Banach space. We find the explicit solutions of the set-valued metric projection operator from the considered 2-d Banach space to its unit closed ball. By these solutions, we will calculate its Mordukhovich derivatives in details.
发表机构
- Shawnee State University（肖尼州立大学）
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