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| 凸函数的支撑凸集及其集映射 | |
| 引用本文： | 陈少白,王文义,毛宗源.凸函数的支撑凸集及其集映射[J].数学杂志,2006,26(5):585-590. |
| 作者姓名： | 陈少白 王文义 毛宗源 |
| 作者单位： | 1. 华南理工大学自动化科学与工程学院,广东广州,510640;武汉科技大学理学院,湖北武汉,430081 2. 武汉船舶职业技术学院电子电气工程系,湖北武汉,430050 3. 华南理工大学自动化科学与工程学院,广东广州,510640 |
| 摘 要： | 本文研究了线性空间中凸函数的支撑泛函存在性以及支撑泛函的数值域,利用子空间中支撑泛函延拓的方法,构造出在线性空间任意点的支撑泛函,确定在同一支撑点上支撑泛函的数值域,从而得到支撑泛函具有唯一性的充分必要条件,最后对支撑凸集到支撑泛函集的集映射进行讨论. |
| 关 键 词： | 凸函数 支撑泛函 数值域 集映射 |
| 文章编号： | 0255-7797（2006）05-0585-06 |
| 收稿时间： | 2004-08-20 |
| 修稿时间： | 2004-08-202005-02-25 |
SUPPORT CONVEX SETS AND SET MAPPINGS FOR CONVEX FUNCTIONS |
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| CHEN Shao-bai,WANG Wen-yi,MAO Zong-yuan.SUPPORT CONVEX SETS AND SET MAPPINGS FOR CONVEX FUNCTIONS[J].Journal of Mathematics,2006,26(5):585-590. | |
| Authors: | CHEN Shao-bai WANG Wen-yi MAO Zong-yuan |
| Institution: | 1. College of Automation and Engineering, South Chain University of Technology, Guangzhou 510640, China;2. College of Sciences, Wuhan University of Science and Technology, Wuhan 430081, China |
| Abstract: | This paper investigates existence of support functional of a convex function in linear spaces and the numerical ranges of the support functionals on a point. We construct support functionals with function extension and establish the numerical ranges of all support functionals on a support point. We present a necessary and sufficient condition for the support functional on a support point being unique. Finally, we discuss set mappings from support convex sets to support function sets. |
| Keywords: | convex function support functional numerical range set mapping |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |