论对数平均数的特征

IF 1.1 3区数学 Q1 MATHEMATICS Results in Mathematics Pub Date : 2024-07-13 DOI:10.1007/s00025-024-02230-3

Timothy Nadhomi, Maciej Sablik, Justyna Sikorska

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引用次数: 0

摘要

在本论文中，我们有兴趣证明著名的 Hermite-Hadamard 不等式（右侧）对于 $\varphi $-凸函数的对应关系。特别是，我们证明了唯一一个Hermite-Hadamard不等式成立且拉格朗日均值在右侧的凸函数是（直到仿射变换）log凸函数。

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On a Characterization of the Logarithmic Mean

In the present note we are interested in proving the counterpart of the (right-hand side of the) celebrated Hermite–Hadamard inequality for $\varphi $-convex functions. In particular, we prove that the only $\varphi $-convex function for which the Hermite–Hadamard inequality holds with the Lagrangian mean on the right-hand side is (up to an affine transformation) the $\log $-convex function.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.

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