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arXiv · 1504.02718

The Weighted Arithmetic Mean-Geometric Mean Inequality is Equivalent to the H\"{o}lder Inequality

Yongtao Li·Xian-Ming Gu·Jianxing Zhao
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Abstract

In the current note, we investigate the mathematical relations among the weighted arithmetic mean-geometric mean (AM-GM) inequality, the H\"{o}lder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM-GM inequality, the weighted power-mean inequality and the H\"{o}lder inequality are fully achieved. The new results are more generalized than those of previous studies.

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Yongtao Li, Xian-Ming Gu, Jianxing Zhao. 2015-04-10. The Weighted Arithmetic Mean-Geometric Mean Inequality is Equivalent to the H\"{o}lder Inequality. https://doi.org/10.3390/sym10090380

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