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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:345

Article

Rezapour, Sh.¹  Hamlbarani, R.¹ 

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

关键词: cone metric space;    normal cones;    non-normal cones;    fixed point;   

DOI  :  10.1016/j.jmaa.2008.04.049

来源: Elsevier

【 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.

【 授权许可】

Free