Remarks on Caristi's fixed point theorem

被引：49
|
作者：
Khamsi, M. A. [1 ]
机构：
[1] Univ Texas El Paso, Dept Math Sci, El Paso, TX 79968 USA
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 1-2期
关键词：
Partially ordered sets; Minimal element; Order preserving mappings; Contraction and nonexpansive mappings; Fixed point; Multivalued mappings; Subadditive functions; PARTIAL ORDERS; MAPPINGS;
D O I：
10.1016/j.na.2008.10.042
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we give a characterization of the existence of minimal elements in partially ordered sets in terms of fixed points of multivalued maps. This characterization shows that the assumptions in Caristi's fixed point theorem can, a priori, be weakened. Finally, we discuss Kirk's problem on an extension of Caristi's theorem and prove a new positive result which illustrates the weakening mentioned before. (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码：227 / 231
页数：5
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