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Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”. (English) Zbl 1145.54045
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.

##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces
##### Keywords:
cone metric space; normal cones; non-normal cones; fixed point