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arXiv · 2006.10816

Inequalities from Lorentz-Finsler norms

Nicusor Minculete·Christian Pfeifer·Nicoleta Voicu
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Abstract

We show that Lorentz-Finsler geometry offers a powerful tool in obtaining inequalities. With this aim, we first point out that a series of famous inequalities such as: the (weighted) arithmetic-geometric mean inequality, Acz\'el's, Popoviciu's and Bellman's inequalities, are all particular cases of a reverse Cauchy-Schwarz, respectively, of a reverse triangle inequality holding in Lorentz-Finsler geometry. Then, we use the same method to prove some completely new inequalities, including two refinements of Acz\'el's inequality.

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Nicusor Minculete, Christian Pfeifer, Nicoleta Voicu. 2020-06-18. Inequalities from Lorentz-Finsler norms. https://doi.org/10.7153/mia-2021-24-26

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