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

Анотація

УДК 514

Нерівності для середньогеометричної дистанційної метрики

Вивчається метрика гіперболічного типу $h_{G,c},$ введена Довгошеєм, Харірі та Вуоріненом. Знайдено найкращу константу $c>0$, для якої ця функція $h_{G,c}$ є метрикою для конкретно вибраного $G$. Наведено декілька точних нерівностей між $h_{G,c}$ та іншими метриками гіперболічного типу, а також запропоновано кілька результатів, що стосуються випадку включення в формі кулі.

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