Inequalities for the geometric-mean distance metric

Oona Rainio

doi:10.3842/umzh.v76i10.7787

Oona Rainio University of Turku, Finland

DOI: https://doi.org/10.3842/umzh.v76i10.7787

Keywords: hyperbolic geometry, hyperbolic metric, hyperbolic type metrics, triangular ratio metric

Abstract

UDC 514

We study a hyperbolic-type metric $h_{G,c}$ introduced by Dovgoshey, Hariri, and Vuorinen and determine the best constant $c>0$ for which this function $h_{G,c}$ is a metric in specifically chosen $G$. We also present several sharp inequalities between $h_{G,c}$ and other hyperbolic-type metrics and offer several results obtained for the ball inclusion.

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