A New Sharp Ostrowski - Gruss Type Inequality

Abstract

Using a Gr¨uss type inequality for Lipschitzian type functions to obtain a sharp Ostrowski-Gr¨uss type inequality in which a unified treatment of sharp integral inequalities for Lipschitzian type functions of mid-point, trapezoid and Simpson type is provided. Applications for cumulative distribution functions are given.

Key words and phrases. Ostrowski-Gr¨uss type inequality, Lipschitzian type function, cumulative distribution function.

2000 Mathematics Subject Classification. 26D15