DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (2): 171-179.

DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

程立新, 张风

Math. Section, Dept. of Public Courses, Jianghan Petro. Inst. Shashi 434102, China

收稿日期:1993-05-15 修回日期:1993-09-06 出版日期:1995-06-25 发布日期:1995-06-25
基金资助:
Supported by a foundation of COGC.

DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

Cheng Lizin, Zhang Feng

Math. Section, Dept. of Public Courses, Jianghan Petro. Inst. Shashi 434102, China

Received:1993-05-15 Revised:1993-09-06 Online:1995-06-25 Published:1995-06-25
Supported by:
Supported by a foundation of COGC.

摘要/Abstract

摘要： Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are(weak) Asplund spaces.

关键词: convex function, differentiability, Banach space, Asplund space

Abstract: Characterizations of differentiability are obtained for continuous convex functions defined on nonempty open convex sets of Banach spaces as a generalization and application of a mumber of mathematicians several years effort, and a characteristic theorem is given for Banach spaces which are(weak) Asplund spaces.

Key words: convex function, differentiability, Banach space, Asplund space

程立新, 张风. DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES[J]. 数学物理学报(英文版), 1995, 15(2): 171-179.

Cheng Lizin, Zhang Feng. DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES[J]. Acta mathematica scientia,Series B, 1995, 15(2): 171-179.

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DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

DIFFERENTIABILITY OF CONVEX FUNCTIONS AND ASPLUND SPACES

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