Ostrowski type inequality for absolutely continuous functions on segments in linear spaces
Bull. Korean Math. Soc. 2008 Vol. 45, No. 4, 763-780 Printed December 1, 2008
Eder Kikianty, Sever S. Dragomir, and Pietro Cerone Victoria University
Abstract : An Ostrowski type inequality is developed for estimating the deviation of the integral mean of an absolutely continuous function, and the linear combination of its values at $k+1$ partition points, on a segment of (real) linear spaces. Several particular cases are provided which recapture some earlier results, along with the results for trapezoidal type inequalities and the classical Ostrowski inequality. Some inequalities are obtained by applying these results for semi-inner products; and some of these inequalities are proven to be sharp.