| 刘琪,包蒙蒙,李欣雨,庄少漠.Lipschitz函数空间中的端点和圆点[J].安徽建筑大学学报,2026,34(2):58-67 |
| Lipschitz函数空间中的端点和圆点 |
| Extreme Points and Rotund Points in the Space of Lipschitz Functions |
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| DOI： |
| 中文关键词: Lipschitz函数空间 端点 圆点 强端点 |
| 英文关键词: Lipschitz function spaces extreme points rotund point strongly extreme point |
| 基金项目:国家自然科学基金项目（72071066）；教育部人文社会科学研究青年基金项目（20YJC630029）；安徽省自然科学基金项目（2008085MG228）；安徽省高校省级自然科学研究项目（2023AH010020）；安徽建筑大学科研基金项目（JZ201416） |
| 作者 | 单位 | | 刘琪 | School of Architecture and Planning,Anhui Jianzhu University,Hefei 230601,China；Anhui Institute of Territorial Spatial Planning and Ecology,HeSchool of Mathematics and Physics,Anqing Normal University,Anqing 246133,Chinafei 230601,China | | 包蒙蒙 | School of Architecture and Planning,Anhui Jianzhu University,Hefei 230601,China；Anhui Institute of Territorial Spatial Planning and Ecology,HeSchool of Mathematics and Physics,Anqing Normal University,Anqing 246133,Chinafei 230601,China | | 李欣雨 | School of Architecture and Planning,Anhui Jianzhu University,Hefei 230601,China；Anhui Institute of Territorial Spatial Planning and Ecology,HeSchool of Mathematics and Physics,Anqing Normal University,Anqing 246133,Chinafei 230601,China | | 庄少漠 | School of Mathematics,Sun Yat-sen University,Guangzhou 510275,China |
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| 中文摘要: |
| 主要对 Lipschitz函数空间中的端点和圆点进行了深入研究。首先，给出了 Lipschitz函数空间单位球面端点的等价特征定理的证明，并建立了Lipschitz对偶空间与赋范线性空间中端点之间的联系。通过分析Lipschitz函数的性质，证明了单位球面上端点集的补集是稠密的，而端点集本身并不稠密。此外，探讨了Lipschitz强端点的性质，指出在特定空间中，端点与强端点是等价的。 |
| 英文摘要: |
| This paper delves into the extreme points and rotund points in the Lipschitz function space. It begins by proving the equivalent characteristic theorem for the extreme points of the unit sphere in the Lipschitz function space and establishes a connection between the Lipschitz dual space and the extreme points in normed linear spaces. By analyzing the properties of Lipschitz functions, it is shown that the complement of the set of extreme points on the unit sphere is dense, whereas the set of extreme points itself is not. Furthermore, the paper explores the properties of Lipschitz strong extreme points, noting that in specific spaces, extreme points and strong extreme points are equivalent. |
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