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2020 One-point hyperbolic-type metrics
Marina Borovikova, Zair Ibragimov, Miguel Jimenez Bravo, Alexandro Luna
Involve 13(1): 117-136 (2020). DOI: 10.2140/involve.2020.13.117

Abstract

We study basic properties of one-parametric families of the j ̃ -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 δ -hyperbolicity, extend to the settings of locally compact noncomplete metric spaces. We also show that these metrics are δ -hyperbolic only if the underlying space is a once-punctured metric space.

Citation

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Marina Borovikova. Zair Ibragimov. Miguel Jimenez Bravo. Alexandro Luna. "One-point hyperbolic-type metrics." Involve 13 (1) 117 - 136, 2020. https://doi.org/10.2140/involve.2020.13.117

Information

Received: 17 June 2019; Revised: 3 October 2019; Accepted: 4 November 2019; Published: 2020
First available in Project Euclid: 20 March 2020

zbMATH: 07172116
MathSciNet: MR4059946
Digital Object Identifier: 10.2140/involve.2020.13.117

Subjects:
Primary: 30F45
Secondary: 30C99, 51F99

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 1 • 2020
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