Inequalities for the geometric-mean distance metric - Rainio, Oona (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 514We 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.