有界线性空间中的Phelps引理

数学物理学报 ›› 2011, Vol. 31 ›› Issue (2): 369-377.

有界线性空间中的Phelps引理

贺飞^{1, 2}|丘京辉¹

1.苏州大学数学科学学院江苏苏州 215006|2.内蒙古大学数学科学学院呼和浩特 010021

收稿日期:2008-12-25 修回日期:2009-11-30 出版日期:2011-04-25 发布日期:2011-04-25
基金资助:
国家自然科学基金(10871141)资助

Generalization of |Phelps' Lemma to Bornological Vector Spaces

HE Fei^{1, 2}| QIU Jing-Hui¹

1.School of Mathematical Sciences, Suzhou University, Jiangsu Suzhou 215006|2.School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021

Received:2008-12-25 Revised:2009-11-30 Online:2011-04-25 Published:2011-04-25
Supported by:
国家自然科学基金(10871141)资助

摘要/Abstract

摘要：

将Phelps引理推广到有界线性空间. 一个直接的应用是获得了Wong推广到有界线性空间中的Ekeland变分原理. 而且Ng和郑在拓扑线性空间中的有效点存在性定理也容易得到. 同时, 给出了一个局部凸空间中的Phelps引理.

关键词: Phelps引理, Ekeland变分原理, 有效点的存在性, 有界线性空间

Abstract:

Phelps' lemma is extended to bornological vector spaces. An immediate application is to re-establish Wong's generalization of Ekeland variational principle to bornological vector spaces. And Ng and Zheng's result on existence of efficient points in topological vector spaces is easily achieved. Meanwhile, a Phelps' lemma in locally convex spaces is obtained.

Key words: Phelps’lemma, Ekeland variational principle, Existence of efficient points, Bornological vector spaces

中图分类号:

46A17

贺飞, 丘京辉. 有界线性空间中的Phelps引理[J]. 数学物理学报, 2011, 31(2): 369-377.

HE Fei, QIU Jing-Hui. Generalization of |Phelps' Lemma to Bornological Vector Spaces[J]. Acta mathematica scientia,Series A, 2011, 31(2): 369-377.

参考文献

[1] Phelps R R. Support cones in Banach spaces and their applications. Advances in Mathematics, 1974, 13: 1--19

[2] Ng K F, Zheng X Y. Existence of efficient points in vector optimization and generalized Bishop-Phelps theorem. Journal of
Optimization Theory and Applications, 2002, 115: 29--47

[3] Hamel A H. Phelps' lemma, Danes' drop theorem and Ekeland's principle in locally convex spaces. Proceedings of the American
Mathematical Society, 2003, 31: 3025--3038

[4] 贺飞, 刘德, 罗成. 局部凸Hausdorff空间中的Drop定理和Phelps引理以及Ekeland变分原理. 数学学报(中文版), 2006, 49(5): 1145--1153

[5] Qiu J H. Local completeness, drop theorem and Ekeland's variational principle. Journal of Mathematical Analysis and Applications, 2005, 311: 23--39

[6] Wong C W. A drop theorem without vector topology. Journal of Mathematical Analysis and Applications, 2007, 329: 452--471

[7] Hogbe-Nlend H. Bornologies and Functional Analysis. Amsterdam: North-Holland, 1977

[8] Penot J P. The drop theorems,the Petal theorem and Ekeland's variational principle. Nonlinear Analysis, 1986, 10(9): 813--822

[9] Georgiev P G. The strong Ekeland variational principle, the strong drop theorem and applications. Journal of Mathematical
Analysis and Applications, 1988, 131(1): 1--21

[10] 郑喜印. 拓扑线性空间中的Drop定理. 数学年刊(A辑), 2000, 21(2): 141--148

[11] 贺飞, 刘德. 拓扑线性空间中的Drop定理和Phelps引理以及Ekeland变分原理. 数学年刊(A辑), 2006, 27(4): 535--542

[12] Carreras Perez P, Bonet J. Barrelled Locally Convex Spaces. Amsterdam: North-Holland, 1987

[13] Qiu J H. Local completeness and drop theorem. Journal of Mathematical Analysis and Applications, 2002, 266: 288--297

[14] Ekeland L. Nonconvex minimization problems. Bulletin of the American Mathematical Society, 1979, 1: 443--474
\REF{
[15]} Danes J. A geometric theorem useful in
nonlinear functional analysis. Boll Un Mat Ital, 1972, {\bf6}:
369--372