THE EQUIVALENCE OF CONE METRIC SPACES AND METRIC SPACES
By Yuqiang Feng, Weicheng Mao. 2010
74 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/c9a0108f32060f7ee028872f5d2e5a3e7f863d6d
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Citations in the corpus
- Various generalizations of metric spaces and fixed point theorems (2015, background): “In 2010, Feng andMao [63] introduced ametric on a conemetric space and then proved that a complete cone metric space is always a complete metric space.”
- Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications (2015, unknown): “Unfortunately, recently these problems became not attractive since some scholars found the equivalence of fixed point results between cone metric spaces and metric spaces, also between cone b-metric spaces and b-metric spaces (see [4, 5, 6, 7, 13, 14]).”
- On cone metric spaces: A survey (2011, result): “We note that there exist other ways of reducing some cone metric results to the respective results in metric spaces, see [84–89], and a remark at the end of the paper.”
- A Note on Various Types of Cones and Fixed Point Results in Cone Metric Spaces (2013, methodology): “It should be noted that each cone metric space over a solid cone is metrizable, as was shown by various methods in [2, 3, 6, 8, 10, 15, 17].”
- Some Equivalences between Cone $b$-Metric Spaces and $b$-Metric Spaces (2013, methodology): “In this paper, we use the method in [13] to introduce another b-metric on the cone b-metric space and then prove some equivalences between them.”