论文标题
Lorentz-Finsler规范的不平等
Inequalities from Lorentz-Finsler norms
论文作者
论文摘要
我们表明，Lorentz-Finsler几何形状为获得不平等的工具提供了强大的工具。以此目的，我们首先指出，一系列著名的不平等现象，例如：（加权的）算术几何不平等，Aczél's，Popoviciu和Bellman的不平等现象，都是反向Cauchy-Cauchy-Schwarz反向的案例，该案例分别是持有反向Triangle的不等式的Lorentz-Finsler geomperry eonsler eonsler geometry。然后，我们使用相同的方法证明了一些全新的不平等现象，包括Aczél不平等的两种改进。
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, Aczél'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 Aczél's inequality.
