an:05299475
Zbl 1145.54045
Rezapour, Sh.; Hamlbarani, R.
Some notes on the paper ``Cone metric spaces and fixed point theorems of contractive mappings''
EN
J. Math. Anal. Appl. 345, No. 2, 719-724 (2008).
00222619
2008
j
54H25
cone metric space; normal cones; non-normal cones; fixed point
Summary: \textit{L. G. Huang} and \textit{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.
Zbl 1118.54022