## IN HONOR OF KY FAN Ekeland's variational principle states that if a Gateaux differentiable Ε½ . function f has a finite lower bound although it need not attain it , then 5 X Ε½ .5 for every β ) 0, there exists some point x such that f x F β. This β β Ε½ . Ε½ .
Ekeland's variational principle in locally complete spaces
β Scribed by Qiu Jing-Hui
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 79 KB
- Volume
- 257
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
We extend Ekeland's variational principle to locally complete locally convex spaces. As an application of the extension, we obtain a drop theorem in locally convex spaces which improves the related known result.
π SIMILAR VOLUMES
The main purpose of this paper is to introduce the concept of F-type topological spaces and to establish a variational principle and a fixed point theorem in the kind of spaces, which extend Ekeland's variational principle and Caristi's fixed point theorem, respectively.
In this paper, we discuss the stability of Ekeland's variational principles for vector-valued and set-valued maps when the dominating cone is a closed pointed convex cone whose interior may be empty. We provide a new approach to the study of the stability of Ekeland's variational principles for vect