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Abstract
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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.
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