We study a hyperbolic type metric hG,c introduced by Dovgoshey, Hariri, and Vuorinen. We find the best constant $c>0$, for which this function hG,c is a metric in specific choices of G. We give several sharp inequalities between hG,c and other hyperbolic type metrics, and also offer a few results related to ball inclusion.
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Oona Rainio (2024) studied this question.
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