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局部凸空间中的Drop定理，Phelps引理和Ekeland变分原理的推广(英文) 被引量：2

Generalizations of Drop Theorem,Phelps' Lemma and Ekeland's Principle in Locally Convex Spaces
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摘要 在局部凸空间框架下,我们利用Drop定理,Phelps引理和Ekeland变分原理的赋范线性空间的形式对其分别进行了推广.并且阐述了这些定理之间以及和它们赋范线性空间的形式之间是等价的. In locally convex spaces, we extend drop theorem, Phelps＇ lemma and Ekeland＇s principle by using their own normed linear spaces versions. Moreover we show that these theorems are equivalent to each other and to their normed linear spaces counterparts.
作者 贺飞 刘德 罗成
机构地区 内蒙古大学理工学院数学系
出处 《数学进展》 CSCD 北大核心 2007年第5期593-598,共6页 Advances in Mathematics（China）
基金 This work is supported by Foundation of Department of Education of Zhejiang Province
关键词 局部凸空间 DROP定理 Phelps引理 EKELAND变分原理 locally convex spaces drop theorem Phelps＇ lemma Ekeland＇s principle
分类号 O177.3 [理学—基础数学]
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参考文献15

  • 1Georgiev, p.G., The strong Ekeland variational principle, the strong drop theorem and applications, J. Math. Anal. and Appl. 1988, 131: 1-21.
  • 2Penot, J.P., The drop theorems, the Petal theorem and Ekeland's variational principle, Nonlinear Anal. 1986, 10: 813-822.
  • 3Phelps, R.R., Support cones in Banach spaces and their applications, Adv. in Math., 1974, 13: 1-19.
  • 4Ekeland, L., Nonconvex minimization problems, Bull. Amer. Mat. Soc. 1979, 1: 443-474.
  • 5Danes, J., A geometric theorem useful in nonlinear functional analysis, Boll. Un. Mat. Ital., 1972, 6: 369-372.
  • 6Hamel, A.H., Phelps' lemma, Danes'drop theorem and Ekeland's principle in locally convex spaces, Proc. Amer. Math. Soc. 2003, 131: 3025-3038.
  • 7Cheng L, zhou Y. and zheng F., Danes' drop theorem in locally convex spaces, Proc. Amer. Math. Soc, 1996, 124: 3699-3702.
  • 8Qiu J.H., Local completeness and drop theorem, J. Math. Anal. Appl, 2002, 266: 288-297.
  • 9Perez Carreras P. and Bonet J., Barrelled Locally Convex Spaces, Amsterdam: North-Holland, 1987.
  • 10Taylor, A.E., Introduction to Functional Analysis(second edition), New York: John Wiley & sons, 1980.

二级参考文献26

  • 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.

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数学进展
2007年 第5期

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