Functional inequalities for the incomplete gamma function

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:385

Article

Baricz, Arpad¹ 

[1] Univ Babes Bolyai, Dept Econ, Cluj Napoca 400591, Romania

关键词: Incomplete gamma function;    Functional inequalities;    Turan-type inequality;    Grunbaum-type inequality;    Power sums;    Power means;    Arithmetic, geometric, and harmonic means;    Convex;    Concave;    Subadditive;    Completely monotonic;   

DOI  :  10.1016/j.jmaa.2011.06.032

来源: Elsevier

【 摘 要 】

We present several inequalities for fa(x) = Gamma(a,x)/Gamma(a,0) (a > 0, x >= 0), where Gamma(a, x) is the incomplete gamma function. One of our theorems states that the inequalities f(a)(S(p)(x(1) (,) ... x(n))) <= f(a)(x(1)) ... f(a)(x(n)) <= fa (Sq (x(1),...,x(n))) (p, q > 0) hold for all nonnegative real numbers x(1),..., x(n) (n >= 2) if and only if p <= min(a, 1) and q >= max(a, 1). Here, S(t)(x(1),..., x(n) denotes the power sum of order t. This extends and complements a result published by Ismail and Laforgia in 2006. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free