Weighted integral and integro-differential inequalities

被引：6
|
作者：
Grinshpan, Arcadii Z. [1 ]
机构：
[1] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA
来源：
ADVANCES IN APPLIED MATHEMATICS | 2008年 / 41卷 / 02期
关键词：
weighted integral inequalities; integro-differential inequalities; opial-type inequalities; beta and gamma functions; incomplete beta and gamma functions; error function; Dawson's integral; confluent hypergeometric function; Erdelyi-Kober integral; Riemann-Liouville integral;
D O I：
10.1016/j.aam.2007.09.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A general weighted integral inequality for two continuous functions on an interval [a, b] is presented. The equality conditions are given. This result implies the new inequalities for the incomplete beta and gamma functions as well a, the related estimates for the confluent hypergeometric function, error function, and Dawson's integral. Also it implies various weighted integro-differential inequalities, those of the Opial type included, and some inequalities which involve the Erdelyi-Kober and Riemann-Liouville fractional integrals. (C) 2007 Elsevier Inc. All rights reserved.
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页码：227 / 246
页数：20
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