The Weighted Arithmetic Mean-Geometric Mean Inequality is Equivalent to the Hölder Inequality
arXiv:1504.02718 · doi:10.3390/sym10090380
Abstract
In the current note, we investigate the mathematical relations among the weighted arithmetic mean-geometric mean (AM-GM) inequality, the Hölder 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 Hölder inequality are fully achieved. The new results are more generalized than those of previous studies.
5 pages. The short note has been initially submitted to journal (Int. J. Anal. Appl.) for peer-review. Finally, the revised manuscript had been published in the journal--Symmetry Sept. 4, 2018