Weighted integral and integro-differential inequalities

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.