Inequalities for the geometric-mean distance metric
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 o...
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| Дата: | 2025 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2025
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7787 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512748446679040 |
|---|---|
| author | Rainio, Oona Rainio, Oona |
| author_facet | Rainio, Oona Rainio, Oona |
| author_sort | Rainio, Oona |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-05-09T12:53:51Z |
| description | 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. |
| doi_str_mv | 10.3842/umzh.v76i10.7787 |
| first_indexed | 2026-03-24T03:33:43Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7787 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:33:43Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-77872025-05-09T12:53:51Z Inequalities for the geometric-mean distance metric Inequalities for the geometric-mean distance metric Rainio, Oona Rainio, Oona hyperbolic geometry hyperbolic metric hyperbolic type metrics triangular ratio metric Hyperbolic geometry 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. 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. Institute of Mathematics, NAS of Ukraine 2025-05-07 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7787 10.3842/umzh.v76i10.7787 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 10 (2024); 1526 -1536 Український математичний журнал; Том 76 № 10 (2024); 1526 -1536 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7787/10219 Copyright (c) 2024 Oona Rainio |
| spellingShingle | Rainio, Oona Rainio, Oona Inequalities for the geometric-mean distance metric |
| title | Inequalities for the geometric-mean distance metric |
| title_alt | Inequalities for the geometric-mean distance metric |
| title_full | Inequalities for the geometric-mean distance metric |
| title_fullStr | Inequalities for the geometric-mean distance metric |
| title_full_unstemmed | Inequalities for the geometric-mean distance metric |
| title_short | Inequalities for the geometric-mean distance metric |
| title_sort | inequalities for the geometric-mean distance metric |
| topic_facet | hyperbolic geometry hyperbolic metric hyperbolic type metrics triangular ratio metric Hyperbolic geometry |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7787 |
| work_keys_str_mv | AT rainiooona inequalitiesforthegeometricmeandistancemetric AT rainiooona inequalitiesforthegeometricmeandistancemetric |