A1 Refereed original research article in a scientific journal

Inequalities and bi-Lipschitz conditions for the triangular ratio metric



Authors: Hariri P, Vuorinen M, Zhang X

Publisher: Rocky Mountain Mathematics Consortium

Publication year: 2017

Journal: Rocky Mountain Journal of Mathematics

Journal name in source: Rocky Mountain Journal of Mathematics

Volume: 47

Issue: 4

First page : 1121

Last page: 1148

Number of pages: 28

ISSN: 0035-7596

eISSN: 1945-3795

DOI: https://doi.org/10.1216/RMJ-2017-47-4-1121


Abstract

Let G ⊆ ℝn be a domain, and let d1 and d2 be two metrics on G. We compare the geometries defined by the two metrics to each other for several pairs of metrics. The metrics we study include the distance ratio metric, the triangular ratio metric and the visual angle metric. Finally, we apply our results to study Lipschitz maps with respect to these metrics.



Last updated on 2024-26-11 at 23:06