Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings"

被引：447

作者：

Rezapour, Sh. ^{[1
]}

Hamlbarani, R. ^{[1
]}

机构：

[1] Azarbaidjan Univ Tarbiat Moallem, Dept Math, Azarshahr, Tabriz, Iran

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 345卷 / 02期

关键词：

cone metric space; normal cones; non-normal cones; fixed point;

D O I：

10.1016/j.jmaa.2008.04.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Huang and Zhang reviewed cone metric spaces in 2007 [Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476]. We shall prove that there are no normal cones with normal constant M < 1 and for each k > 1 there are cones with normal constant M > k. Also, by providing non-normal cones and omitting the assumption of normality in some results of [Huang Long-Guang, Zhang Man, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476], we obtain generalizations of the results. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：719 / 724

页数：6