# Some inequalities involving interpolations between arithmetic and geometric mean

In: Tatra Mountains Mathematical Publications, vol. 81, no. 1
Hongliang Zuo - Yuwei Li
Detaily:
Rok, strany: 2022, 93 - 106
Jazyk: eng
Kľúčové slová:
the weighted power mean, Heron mean, Heinz mean, operator inequalities
Typ článku: Real Functions
Typ dokumentu: scientific paper pdf
O článku:
In this article, we mainly study the interpolations between arithmetic mean and geometric mean—power mean, Heron mean and Heinz mean. First, we obtain the improvement and reverse improvement of arithmetic-power mean inequalities by the convexity of the function. We show that the proof of Heron mean inequality due to Yang and Ren: [\textit{Some results of Heron mean and Young's inequalities}, J. Inequal. Appl. \textbf{2018} (2018), paper no, 172], is not substantial. In addition, we also obtain Heron-Heinz mean inequalities for $t\in\mathbb{R}$. Further corresponding operator versions and generalizations are also established.
Ako citovať:
ISO 690:
Zuo, H., Li, Y. 2022. Some inequalities involving interpolations between arithmetic and geometric mean. In Tatra Mountains Mathematical Publications, vol. 81, no.1, pp. 93-106. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2022-0007

APA:
Zuo, H., Li, Y. (2022). Some inequalities involving interpolations between arithmetic and geometric mean. Tatra Mountains Mathematical Publications, 81(1), 93-106. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2022-0007
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 22. 11. 2022
Verejná licencia:
https://creativecommons.org/licenses/by-nc-nd/4.0/