Asplund空间中方向上导数和序列法紧性质分析法则

龙莆均; 杨新民; 王炳武

doi:10.21656/1000-0887.370238

Asplund空间中方向上导数和序列法紧性质分析法则

doi: 10.21656/1000-0887.370238

¹内蒙古大学数学科学学院, 呼和浩特 010021;²重庆师范大学数学科学学院, 重庆 400047;³东密歇根大学数学学院, 密歇根伊普西兰蒂 48197, 美国

基金项目: 国家自然科学基金（重点项目）(11431004)

详细信息

作者简介:
龙莆均（1987—），男，博士生(E-mail: longpujun@gmail.com)；杨新民（1960—），男，教授(通讯作者. E-mail: xmyang@cqnu.edu.cn)；王炳武（1971—），男，教授(E-mail: bwang@emich.edu).

中图分类号: O221.6
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出版历程
- 收稿日期: 2016-07-28
- 修回日期: 2016-10-17
- 刊出日期: 2017-04-15

Calculus of Normal Cones and Coderivatives Under the Assumption of Directional Inner Semicompactness in Asplund Spaces

Funds: The National Natural Science Foundation of China(Key Program)(11431004)

摘要

摘要: 研究了广义微分结构中的集合方向Mordukhovich法锥、集值映射的方向上导数，以及集合和集值映射的方向序列法紧性的分析法则. 基于集合方向Mordukhovich法锥的交集法则，在方向内半紧性假设下，建立了集合的方向Mordukhovich法锥、集值映射的方向上导数的分析法则.此外，借助Asplund乘积空间中集合的方向序列法紧性的交集法则，在方向内半紧性和相应的规范条件下，建立了集合和集值映射的(部分)方向序列法紧性的加法、逆像、复合等法则.
- 方向内半紧性 /
- 方向Mordukhovich法锥 /
- 方向Mordukhovich上导数 /
- 方向(部分)序列法紧性
Abstract: The directional Mordukhovich normal cones of sets, directional Mordukhovich coderivatives of set-valued mapping, and directional sequential normal compactness of sets and set-valued mapping in the framework of generalized differentiation were studied. Based on the intersection rule for directional Mordukhovich normal cones of sets, the calculus rules on directional Mordukhovich normal cones of sets and directional Mordukhovich coderivatives of set-valued mapping were established under some directional inner semicompactness assumptions. Furthermore, in virtue of the intersection rule for directional sequential normal compactness of sets, the sum rule, inverse mapping rule, and composition rule for directional (partial) sequential normal compactness of sets and set-valued mapping were presented under some directional inner semicompactness assumptions and suitable qualification conditions.

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参考文献(24)

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Asplund空间中方向上导数和序列法紧性质分析法则

doi: 10.21656/1000-0887.370238

作者简介:
龙莆均（1987—），男，博士生(E-mail: longpujun@gmail.com)；杨新民（1960—），男，教授(通讯作者. E-mail: xmyang@cqnu.edu.cn)；王炳武（1971—），男，教授(E-mail: bwang@emich.edu).

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Calculus of Normal Cones and Coderivatives Under the Assumption of Directional Inner Semicompactness in Asplund Spaces

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目录

留言板

Asplund空间中方向上导数和序列法紧性质分析法则

doi: 10.21656/1000-0887.370238

作者简介: 龙莆均（1987—），男，博士生(E-mail: longpujun@gmail.com)；杨新民（1960—），男，教授(通讯作者. E-mail: xmyang@cqnu.edu.cn)；王炳武（1971—），男，教授(E-mail: bwang@emich.edu).

计量

出版历程

Calculus of Normal Cones and Coderivatives Under the Assumption of Directional Inner Semicompactness in Asplund Spaces

计量

出版历程

目录

作者简介:
龙莆均（1987—），男，博士生(E-mail: longpujun@gmail.com)；杨新民（1960—），男，教授(通讯作者. E-mail: xmyang@cqnu.edu.cn)；王炳武（1971—），男，教授(E-mail: bwang@emich.edu).