On certain new refinements of Finsler-Hadwiger inequalities

Several refinements of the Finsler-Hadwiger inequality and its reverse in the triangle are discussed. A new one parameter family of Finsler-Hadwiger inequalities and their reverses are proved. This allows us to obtain new bounds for the sum of the squares of the side lengths of a triangle in terms o...

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Detalles Bibliográficos
Autor principal: Kouba, Omran
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5395604/
https://www.ncbi.nlm.nih.gov/pubmed/28479832
http://dx.doi.org/10.1186/s13660-017-1356-5
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author Kouba, Omran
author_facet Kouba, Omran
author_sort Kouba, Omran
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description Several refinements of the Finsler-Hadwiger inequality and its reverse in the triangle are discussed. A new one parameter family of Finsler-Hadwiger inequalities and their reverses are proved. This allows us to obtain new bounds for the sum of the squares of the side lengths of a triangle in terms of other elements in the triangle. Finally, these new bounds are compared to known ones.
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spelling pubmed-53956042017-05-04 On certain new refinements of Finsler-Hadwiger inequalities Kouba, Omran J Inequal Appl Research Several refinements of the Finsler-Hadwiger inequality and its reverse in the triangle are discussed. A new one parameter family of Finsler-Hadwiger inequalities and their reverses are proved. This allows us to obtain new bounds for the sum of the squares of the side lengths of a triangle in terms of other elements in the triangle. Finally, these new bounds are compared to known ones. Springer International Publishing 2017-04-18 2017 /pmc/articles/PMC5395604/ /pubmed/28479832 http://dx.doi.org/10.1186/s13660-017-1356-5 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Kouba, Omran
On certain new refinements of Finsler-Hadwiger inequalities
title On certain new refinements of Finsler-Hadwiger inequalities
title_full On certain new refinements of Finsler-Hadwiger inequalities
title_fullStr On certain new refinements of Finsler-Hadwiger inequalities
title_full_unstemmed On certain new refinements of Finsler-Hadwiger inequalities
title_short On certain new refinements of Finsler-Hadwiger inequalities
title_sort on certain new refinements of finsler-hadwiger inequalities
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5395604/
https://www.ncbi.nlm.nih.gov/pubmed/28479832
http://dx.doi.org/10.1186/s13660-017-1356-5
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