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One-point
hyperbolic-type metrics
Marina Borovikova, Zair Ibragimov, Miguel Jimenez Bravo and Alexandro Luna
Vol. 13 (2020), No. 1, 117–136
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Abstract |
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We study basic properties of one-parametric families of the -metric, the scale-invariant Cassinian metric and the half-Apollonian metric on locally compact, noncomplete metric spaces. We first establish basic properties of these metrics on once-punctured general metric spaces and obtain sharp estimates between these metrics, and then we show that all these properties, except for -hyperbolicity, extend to the settings of locally compact noncomplete metric spaces. We also show that these metrics are -hyperbolic only if the underlying space is a once-punctured metric space. |
Keywords
semimetric spaces, metric spaces, Ptolemaic spaces,
$\delta$-hyperbolic spaces, half-Apollonian metric, $\tilde
j$-metric, scale-invariant Cassinian metric
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Mathematical Subject Classification 2010
Primary: 30F45
Secondary: 51F99, 30C99
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Milestones
Received: 17 June 2019
Revised: 3 October 2019
Accepted: 4 November 2019
Published: 4 February 2020
Communicated by Kenneth S. Berenhaut
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Authors |
| Marina Borovikova | |
| Department of Mathematics California State University Fullerton, CA United States |
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| Zair Ibragimov | |
| Department of Mathematics California State University Fullerton, CA United States |
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| Miguel Jimenez Bravo | |
| Department of Mathematics California State University Fullerton, CA United States |
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| Alexandro Luna | |
| Department of Mathematics California State University Fullerton, CA United States |
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