Ostrowski Type Inequality for Absolutely Continuous Functions on Segments in Linear Spaces

Abstract

An Ostrowski type inequality is developed for estimating the devi- ation of the integral mean of an absolutely continuous function and the linear combination of its values at k + 1 partition points on a segment in (real) linear spaces. Some particular cases are provided which recapture earlier re- sults along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Inequalities are obtained by applying these results for semi-inner products and some of these inequalities are proven to be sharp