A note on a paper of ID Arandelovic on asymptotic contractions

被引：8

作者：

Jachymski, Jacek ^{[1
]}

机构：

[1] Tech Univ Lodz, Inst Math, PL-93005 Lodz, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 358卷 / 02期

关键词：

Asymptotic fixed point theory; Asymptotic contractions; Fixed point; Complete metric space; FIXED-POINT THEOREM; MEIR-KEELER TYPE; METRIC-SPACES; END-POINTS;

D O I：

10.1016/j.jmaa.2009.05.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

W.A. Kirk [W.A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl. 277 (2003) 645-650] defined the notion of an asymptotic contraction oil a metric space and using ultrapower techniques lie gave a nonconstructive proof of an asymptotic version of the Boyd-Wong fixed point theorem. Subsequently, I.D. Arandelovic [I.D. Arandelovic, On a fixed point theorem of Kirk, J. Math. Anal. Appl. 301 (2005) 384-385] established somewhat more general version of Kirk's result and lie gave an elementary proof of it, However, our purpose is to show that there is an error in this proof and, moreover, Arandelovic's theorem is false. We also explain how to correct this result. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：491 / 492

页数：2

共 9 条

[1] On a fixed point theorem of Kirk [J].