Convexity of the gamma function with respect to Holder means

被引：0

作者：

Trif, T ^{[1
]}

机构：

[1] Univ Babes Bolyai, Fac Matemat Informat, Cluj Napoca, Romania

来源：

INEQUALITY THEORY AND APPLICATIONS VOL 3 | 2003年

关键词：

gamma function; digamma function; multiplicatively convex function; geometrically convex function;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the gamma function is strictly multiplicatively concave on [0, x(0)] and strictly multiplicatively convex on [x(0), infinity], where x(0) is an element of [0, 1] is the unique solution of the equation psi(x) + xpsi'(x) = 0 and psi : [0, infinity] --> R is the digamma function: psi(x) = (dx)-(d) logGamma(x). Thus we answer to an open question raised by C. P. Niculescu [6, p. 164]. Likewise, we investigate the convexity of Gamma with respect to the Holder means.

引用

页码：189 / 195

页数：7

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