Authors: Jing Hui Qiu Fei He
Publish Date: 2011/10/24
Volume: 28, Issue: 2, Pages: 235-254
Abstract
In this paper we attempt to give a unified approach to the existing several versions of Ekeland’s variational principle In the framework of uniform spaces we introduce pdistances and more generally qdistances Then we introduce a new type of completeness for uniform spaces ie sequential completeness with respect to a qdistance particularly a pdistance which is a very extensive concept of completeness By using qdistances and the new type of completeness we prove a generalized Takahashi’s nonconvex minimization theorem a generalized Ekeland’s variational principle and a generalized Caristi’s fixed point theorem Moreover we show that the above three theorems are equivalent to each other From the generalized Ekeland’s variational principle we deduce a number of particular versions of Ekeland’s principle which include many known versions of the principle and their improvements
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