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Inequalities from Lorentz-Finsler norms

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arxiv 2006.10816 v2 pith:FQ2HCYQB submitted 2020-06-18 math.DG

Nicusor Minculete , Christian Pfeifer , Nicoleta Voicu This is my paper · ORCID
classification math.DG
keywords inequalitiesinequalitylorentz-finslergeometryreversearithmetic-geometricbellmancases
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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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