Results 281 to 290 of about 902,467 (342)

A Power Mean Inequality for the Gamma Function

Monatshefte f�r Mathematik, 2000
In this interesting paper, the author extends a result due to \textit{L. G. Lucht} [Aequationes Math. 39, No. 2/3, 204-209 (1990; Zbl 0705.39002)] on convexity-like inequalities for Euler's gamma function, involving the geometric mean. Let \(x_j>0,\;p_j>0\;(1\leq j\leq n),\;p_1+\cdots +p_n=1\) and \(n\geq 2\).
Horst Alzer
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Generalizations of mixed weighted power mean inequality [PDF]

Journal of Shanghai University (English Edition), 2006
Tamavas established mixed weighted power mean inequality in 1999. A separation of weighted power mean inequality was derived in this paper. As its applications, some separations of other inequalities were given.
马统一, 张海娟
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On refinements of some integral inequalities using improved power‐mean integral inequalities

Numerical Methods for Partial Differential Equations, 2020
In this study, using power‐mean inequality and improved power‐mean integral inequality better approach than power‐mean inequality and an identity for differentiable functions, we get inequalities for functions whose derivatives in absolute value at ...
H. Kadakal
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Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality

Journal of Applied Analysis, 2019
In this paper, we establish fractional Ostrowski’s inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality.
Badreddine Meftah
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The reverse Hölder inequality for power means [PDF]

Journal of Mathematical Sciences, 2012
For a function φ non-negative on the interval [0, 1], the power mean of order α ≠ 0 is defined by the equality \( \mathcal{M}_{\alpha \varphi} (t) = {\left( {\frac{1}{t}\int_0^t {{\varphi^\alpha }(u)du} } \right)^{1/\alpha }},\,0 < t \leqslant 1 \). We consider the class \( {\widetilde{{RH}}^{\alpha, \beta }}(B) \)of functions φ satisfying the reverse ...
Anatolii A. Korenovskyi, Viktor D. Didenko   +1 more
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Power Mean Inequalities and Sums of Squares

Discrete & Computational Geometry
For fixed degree and increasing number of variables the dimension of the vector space of $n$-variate real symmetric homogeneous polynomials (forms) of degree $d$ stabilizes. We study the limits of the cones of symmetric nonnegative polynomials and symmetric sums of squares, when expressed in power-mean or monomial-mean basis. These limits correspond to
José Antonio Acevedo-Suárez, Grigoriy Blekherman   +1 more
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Inequalities for differences of power means in two variables [PDF]

Analysis Mathematica, 2011
Using classical analytic techniques, a double inequality for differences of power means and geometric means in two variables is generalized and sharpened. A new inequality for differences of power means involving four parameters is established.
Shanhe Wu, Lokenath Debnath
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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
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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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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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