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Search Results (3)

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Keywords = arithmetic mean-geometric mean (AM-GM) inequality

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9 pages, 252 KiB  
Article
On a New Integral Inequality: Generalizations and Applications
by Huaping Huang and Wei-Shih Du
Axioms 2022, 11(9), 458; https://doi.org/10.3390/axioms11090458 - 6 Sep 2022
Cited by 3 | Viewed by 1856
Abstract
In this paper, we present some generalizations and improvements of a new integral inequality from the 29th IMC in 2022. Some applications of our new results are also provided. Full article
(This article belongs to the Special Issue Special Issue in Honor of the 60th Birthday of Professor Hong-Kun Xu)
12 pages, 272 KiB  
Article
On New Generalized Dunkel Type Integral Inequalities with Applications
by Dong-Sheng Wang, Huan-Nan Shi, Chun-Ru Fu and Wei-Shih Du
Symmetry 2021, 13(9), 1576; https://doi.org/10.3390/sym13091576 - 27 Aug 2021
Viewed by 1942
Abstract
In this paper, by applying majorization theory, we study the Schur convexity of functions related to Dunkel integral inequality. We establish some new generalized Dunkel type integral inequalities and their applications to inequality theory. Full article
(This article belongs to the Special Issue Integral Transformation, Operational Calculus and Their Applications)
5 pages, 216 KiB  
Article
The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality
by Yongtao Li, Xian-Ming Gu and Jianxing Zhao
Symmetry 2018, 10(9), 380; https://doi.org/10.3390/sym10090380 - 4 Sep 2018
Cited by 14 | Viewed by 5258
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 [...] Read more.
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. Full article
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