Conditions for convexity of a derivative and some applications to the Gamma function

被引：0
|
作者：
Merkle M. [1 ]
机构：
[1] University of Belgrade, Faculty of Electrical Engineering, Department of Applied Mathematics, 11120 Belgrade
来源：
aequationes mathematicae | 1998年 / 55卷 / 3期
关键词：
Convexity; Gamma function; Inequalities; Schur-convexity;
D O I：
10.1007/s000100050036
中图分类号：
学科分类号：
摘要：
We consider necessary and sufficient conditions for the convexity of a function x f′(x) in terms of some properties of the associated function of two variables F (x,y) = (f (y) - f(x))/(y - x)- In particular, we prove that f′ is convex if and only if F is convex and if and only if F is Schur-convex. These results are applied to the theory of the Gamma function. We complement a characterization of the Gamma function due to H. Kairies and present some inequalities for the ratio of Gamma functions. © Birkhäuser Verlag, Basel, 1998.
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页码：273 / 280
页数：7
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