On Ha's Version of Set-valued Ekeland's Variational Principle

被引：0

作者：

Jing Hui QIU ^{[1
]}

机构：

[1] School of Mathematic Science, Soochow University

来源：

Acta Mathematica Sinica,English Series | 2012年 / 28卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Ekeland’s variational principle; set-valued map; locally convex space; Caristi–Kirk’s fixed point theorem; Takahashi’s nonconvex minimization theorem;

D O I：

暂无

中图分类号：

O174 [函数论];

学科分类号：

070104 ;

摘要：

By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational principle for a set-valued map. J. Optim. Theory Appl., 124, 187-206 (2005)] established a new version of Ekeland’s variational principle for set-valued maps, which is expressed by the existence of strict approximate minimizer for a set-valued optimization problem. In this paper, we give an improvement of Ha’s version of set-valued Ekeland’s variational principle. Our proof is direct and it need not use Dancs-Hegedus-Medvegyev theorem. From the improved Ha’s version, we deduce a Caristi-Kirk’s fixed point theorem and a Takahashi’s nonconvex minimization theorem for set-valued maps. Moreover, we prove that the above three theorems are equivalent to each other.

引用

页码：717 / 726

页数：10

共 15 条

[1] Some generalizations of Caristi's fixed point theorem with applications to the fixed point theory of weakly contractive set-valued maps and the minimization problem [J].