首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Phelps' lemma, Danes' drop theorem and Ekeland's principle in locally convex spaces
Authors:Andreas H Hamel
Institution:Department of Mathematics and Computer Sciences, Martin-Luther-University Halle-Wittenberg, Theodor-Lieser-Str. 5, D-06099 Halle, Germany
Abstract:A generalization of Phelps' lemma to locally convex spaces is proven, applying its well-known Banach space version. We show the equivalence of this theorem, Ekeland's principle and Danes' drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto efficiency theorem due to Isac. This solves a problem, concerning the drop theorem, proposed by G. Isac in 1997.

We show that a different formulation of Ekeland's principle in locally convex spaces, using a family of topology generating seminorms as perturbation functions rather than a single (in general discontinuous) Minkowski functional, turns out to be equivalent to the original version.

Keywords:Phelps' lemma  Ekeland's variational principle  Dane\u{s}' drop theorem  efficiency  locally convex space
点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号