Local completeness, drop theorem and Ekeland's variational principle

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:311

Article

Qiu, JH

关键词: locally convex spaces;    local completeness;    drop theorem;    Ekeland's variational principle;   

DOI  :  10.1016/j.jmaa.2004.12.045

来源: Elsevier

【 摘 要 】

By using a very general drop theorem in locally convex spaces we obtain some extended versions of Ekeland's variational principle, which only need assume local completeness of some related sets and improve Hamel's recent results. From this, we derive some new versions of Caristi's fixed points theorems. In the framework of locally convex spaces, we prove that Danes' drop theorem, Ekeland's variational principle, Caristi's fixed points theorem and Phelps lemma are equivalent to each other. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free