Rezapour, Sh.; Hamlbarani, R. Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”. (English) Zbl 1145.54045 J. Math. Anal. Appl. 345, No. 2, 719-724 (2008). Summary: L. G. Huang and X. Zhang [J. Math. Anal. Appl. 332, No. 2, 1468–1476 (2007; Zbl 1118.54022)] reviewed cone metric spaces. We 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 [loc. cit.], we obtain generalizations of the results. Cited in 13 ReviewsCited in 220 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) Keywords:cone metric space; normal cones; non-normal cones; fixed point Citations:Zbl 1118.54022 PDF BibTeX XML Cite \textit{Sh. Rezapour} and \textit{R. Hamlbarani}, J. Math. Anal. Appl. 345, No. 2, 719--724 (2008; Zbl 1145.54045) Full Text: DOI OpenURL References: [1] Long-Guang, Huang; Xian, Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. math. anal. appl., 332, 1468-1476, (2007) · Zbl 1118.54022 [2] Mohebi, H., Topical functions and their properties in a class of ordered Banach spaces, (), 343-361 · Zbl 1124.90048 [3] Mohebi, H.; Sadeghi, H.; Rubinov, A.M., Best approximation in a class of normed spaces with star-shaped cone, Numer. funct. anal. optim., 27, 3-4, 411-436, (2006) · Zbl 1098.41036 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.