Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings" S W Article 0.10% %
Rezapour Sh., Hamlbarani R.
Journal of Mathematical Analysis and Applications Volume 345, Issue 2, 2008 , Pages 719-724
(IF=1.064 ,,JCR2016) (CiteScore=1.11 ,Quartile 2,Scopus2016)
Abstract:
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 Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476], we obtain generalizations of the results. © 2008 Elsevier Inc. All rights reserved.
Keywords :
Cone metric space; Fixed point; Non-normal cones; Normal cones