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<p>We study a hyperbolic-type metric <i>h</i><sub><i>G,c</i></sub> introduced by Dovgoshey, Hariri, and Vuorinen and determine the best constant <i>c</i> &gt; 0 for which this function <i>h</i><sub><i>G,c</i></sub> is a metric in specifically chosen <i>G</i>. We also present several sharp inequalities between <i>h</i><sub><i>G,c</i></sub> and other hyperbolic-type metrics and offer several results obtained for a ball inclusion.</p>

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Inequalities for the Geometric-Mean Distance Metric

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Oona Rainio

摘要

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