Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings” |
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Authors: | Sh Rezapour R Hamlbarani |
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Institution: | Department of Mathematics, Azarbaidjan University of Tarbiat Moallem, Azarshahr, Tabriz, Iran |
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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. |
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Keywords: | Cone metric space Normal cones Non-normal cones Fixed point |
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