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有界线性空间中的Phelps引理

Generalization of Phelps' Lemma to Bornological Vector Spaces
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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. 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.
作者 贺飞 丘京辉
机构地区 苏州大学数学科学学院 内蒙古大学数学科学学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2011年第2期369-377,共9页 Acta Mathematica Scientia
基金 国家自然科学基金(10871141)资助
关键词 Phelps引理 EKELAND变分原理 有效点的存在性 有界线性空间 Phelps＇ lemma Ekeland variational principle Existence of efficient points Bornological vector spaces.
分类号 O177.3 [理学—基础数学]
  • 相关文献

参考文献15

  • 1Phelps R R.Support cones in Banach spaces and their applications.Advances in Mathematics,1974,13:1-19.
  • 2Ng 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.
  • 3Hamel A H.Phelps' lemma,Danes' drop theorem and Ekeland's principle in locally convex spaces.Proceedings of the American Mathematical Society,2003,131:3025-3038.
  • 4贺飞,刘德,罗成.局部凸空间中的Drop定理和Phelps引理以及Ekeland变分原理[J].数学学报（中文版）,2006,49(5):1145-1152. 被引量：6
  • 5Qiu J H.Local completeness,drop theorem and Ekeland's variational principle.Journal of Mathematical Analysis and Applications,2005,311:23-39.
  • 6Wong C W.A drop theorem without vector topology.Journal of Mathematical Analysis and Applications,2007,329:452-471.
  • 7Hogbe-Nlend H.Bornologies and Functional Analysis.Amsterdam:North-Holland,1977.
  • 8Penot J P.The drop theorems,the Petal theorem and Ekeland's variational principle.Nonlinear Analysis,1986,10(9):813-822.
  • 9Georgiev 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[J].数学年刊（A辑）,2000,1(2):141-148. 被引量：7

二级参考文献28

  • 1Danes J., A geometric throrem useful in nonlinear fuctional analysis [J], Boll. Un. Mat.Ital., 1972, 13:369-372.
  • 2Penot J. P., The drop theorems, the Petal theorem and Ekeland's variational principle[J], Non. Anal., 1986, 10:813-822.
  • 3Georgiev P. G., The strong Ekeland variational principle, the strong drop theorem and applications [J], J. Math. Anal. Appl., 1988, 131:1-21.
  • 4Cheng L. X., Zhou Y. C. and Zhang F., Danes' drop theorem in locally convex spaces[J], Proc. Amer. Math. Soc., 1996, 124:3699-3702.
  • 5Qiu J. H., Local Completeness and drop theorem [J], J. Math. Anal. Appl., 2002,266:288-297.
  • 6Ekeland L., Noneonvex minimization problems [J], Bull. Amer. Mat. Soc., 1979,1(3):443-474.
  • 7Phelps R. R., Support cones in Banach spaces and their applications [J], Adv. Math.,1974, 13:1-19.
  • 8Isac G., Ekeland's principal and nuclear cones: A geometrical aspect [J], Mathematical and Computer Modelling, 1997, 26(11):111-116.
  • 9Hamel A. H., Phelps' lemma, Danes' drop theorem and Ekeland's principle in locally convex spaces [J], Proc. Amer. Math. Soc., 2003, 131(10):3025-3038.
  • 10Taylor A. E., Introduction to Fuctional Analysis (Second Edition) [M], New York: John Wiley & Sons, 1980.

共引文献11

数学物理学报（A辑）
2011年 第2期

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