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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 275806, 8 pages
http://dx.doi.org/10.1155/2014/275806
Research Article

On New Generalized Ostrowski Type Integral Inequalities

1Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia
2Department of Mathematics, University of Ha’il, P.O. Box 2440, Ha’il 81451, Saudi Arabia
3School of Computational and Applied Mathematics, University of the Witwatersrand (Wits), Private Bag 3, Johannesburg 2050, South Africa

Received 26 February 2014; Revised 30 March 2014; Accepted 6 May 2014; Published 22 May 2014

Academic Editor: Elena Berdysheva

Copyright © 2014 A. Qayyum et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequality. The current paper obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval in terms of the norms of the second derivative of the function. Some new perturbed results are obtained. Application for cumulative distribution function is also discussed.