Results 261 to 270 of about 36,503 (284)

Generalizations of mixed weighted power mean inequality

Journal of Shanghai University, 2006
Let \(x=\left( x_{1},x_{2},\dots ,x_{n}\right) \), \(q=\left( q_{1},q_{2},\dots ,q_{n}\right) ,\) with \(x_{i}>0,q_{i}>0\) \(\left( i=1,2,\dots ,n\right) \) and \(a\) be a real number. Denote \(Q_{n}= \sum_{i=1}^{n}q_{i},\) \[ M_{n}^{[a]}(x;q)=\begin{cases} \left( \frac{1}{Q_{n}}\sum_{i=1}^{n}q_{i}x_{i}^{a}\right) ^{{1}/{a}},&a\neq 0, \\ \left( \prod_ ...
Ma, Tongyi, Zhang, Haijuan
exaly   +3 more sources

The Power Mean Inequality

, 1996
openaire   +2 more sources

The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality

Symmetry, 2018
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.
Xian-Ming Gu, Jianxing Zhao, Zhao Jianxing   +2 more
exaly   +2 more sources

Means of Power Type and Their Inequalities

Mathematische Nachrichten, 1999
AbstractWe prove some general results on means of power type and their inequalities. Particularly, we study a new mean and compare this mean with the classical power means. Some results connected to compositions of power means are also presented. Our results are applied to some inequalities in the homogenization theory.
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The reverse Hölder inequality for power means

Journal of Mathematical Sciences, 2012
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Didenko, Viktor D., Korenovskyi, Anatolii A.   +1 more
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Power means and the reverse Hölder inequality

Studia Mathematica, 2011
Let w be a non-negative measurable function defined on the positive semi-axis and satisfying the reverse Holder inequality with exponents 0 0, are obtained for various exponents α. As a result, for the function w a property of the self-improvement of the summability exponents is established.
Victor D. Didenko, Anatolii A. Korenovskyi   +1 more
openaire   +1 more source

Some Inequalities for Matrix Power Means

Bulletin of the Iranian Mathematical Society, 2019
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Matrix inequalities related to power means of probability measures

Linear and Multilinear Algebra, 2021
For a probability measure of compact support μ on the set Pn of all positive definite matrices and t∈(0,1], let Pt(μ) be the unique positive solution of X=∫PnX♯tZdμ(Z).
Mohsen Kian, Mohammad Sal Moslehian
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Reverse inequalities for geometric and power means

Ukrainian Mathematical Journal, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Inequalities for differences of power means in two variables

Analysis Mathematica, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Shanhe, Debnath, Lokenath
openaire   +2 more sources