Some inequalities involving weighted power mean: Real Functions and Algebra

Strany: 205 - 218

Jazyk: eng

In this paper, we first show some inequalities on weighted power mean. When $a,b ≥ 0$, $p≥ 1$ and $0 ≤ v ≤ τ ≤ 1$, we have

$$ ((v) / (τ)) ≤ \frac{{a{\sharp_p,v}b-a{\sharp_v}b}} {{a{\sharp_p,τ}b-a{\sharp_τ}b}} ≤ \frac{{1 - v}}{{1 - τ}} $$ and

$$ ((v) / (τ)) ≤ \frac{{a{\sharp_p,v}b-a{!_v}b}} {{a{\sharp_p,τ}b-a{!_τ}b}} ≤ \frac{{1 - v}}{{1-τ}}. $$ Further, we obtain the range of corresponding inequalities involving the $m$ power form of weighted power mean in the same form as above for $m \in {\mathbb{N}}⁺$ or $p≥ m ≥ 0$, $m≤ p ≤ 0$. As further applications, we provide some inequalities about matrices and determinants, respectively.

ISO 690:

Zuo, H., Niu, X. 2033. Some inequalities involving weighted power mean: Real Functions and Algebra. In Tatra Mountains Mathematical Publications, vol. 86, no.1, pp. 205-218. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2024-0019

APA:

Zuo, H., Niu, X. (2033). Some inequalities involving weighted power mean: Real Functions and Algebra. Tatra Mountains Mathematical Publications, 86(1), 205-218. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2024-0019

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

https://creativecommons.org/licenses/by-nc-nd/4.0/