广东工业大学学报 ›› 2016, Vol. 33 ›› Issue (01): 73-76.doi: 10.3969/j.issn.1007-7162.2016.01.014

• 综合研究 • 上一篇    下一篇

非自反Banach空间中的Lagrange型凸泛函

龚丽燕，张秋园   

  1. 广东工业大学 应用数学学院，广东 广州 510520
  • 收稿日期:2014-05-29 出版日期:2016-01-16 发布日期:2016-01-16
  • 作者简介:龚丽燕（1989-），女，硕士研究生，主要研究方向为非线性泛函分析.

Lagrange Convex Functional in Non-reflexive Banach Space

Gong Li-yan, Zhang Qiu-yuan   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2014-05-29 Online:2016-01-16 Published:2016-01-16

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摘要： 在非自反Banach空间X中讨论了Lagrange型凸泛函及其对偶的一些性质.引入了两个广义次微分概念，进一步研究了它们之间的关系，并指出了非自反Banach空间中的Lagrange型凸泛函具有B自对偶性.

关键词: 非自反Banach空间； 弱*下半连续； 凸泛函

Abstract: This paper discusses the Lagrange convex functional and the duality property in non-reflexive Banach space. In the discussion, two concepts about generalized subdifferential have been introduced and their relationship has been studied. Also it is pointed out that the Lagrange convex functional has the B-self-dual property.

Key words: non-reflexive Banach space; weak*lower semi-continuous; convex functional

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