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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.
Dag Lukkassen
exaly   +2 more sources

A Power Mean Inequality for the Gamma Function

Monatshefte Fur 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
exaly   +2 more sources

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