IJPAM: Volume 98, No. 2 (2015)

A GENERALIZATION OF OSTROWSKI TYPE INEQUALITY
FOR MAPPINGS WHOSE SECOND DERIVATIVES BELONG
TO L $_{1}\left( a,b\right) $ AND APPLICATIONS

A. Qayyum$^1$, I. Faye$^2$, M. Shoaib$^3$, M.A. Latif$^4$
$^{1,2}$Department of Fundamental and Applied Sciences
Petronas University of Teknologi
Bandar Seri Iskandar, 31750 Tronoh, Perak, MALAYSIA
$^3$Department of Mathematics
University of Hail
P.O. Box 2440, KINGDOM OF SAUDI ARABIA
$^4$School of Computational and Applied Mathematics
University of the Witwatersrand
Private Bag 3, Wits 2050, Johannesburg, SOUTH AFRICA


Abstract. In this paper, we will improve and generalize inequality of Ostrowski type for mappings whose second derivatives belong to L $_{1}\left( a,b\right) $. Some well known inequalities can be derived as special cases. In addition, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. The obtained inequalities have immediate applications in numerical integration where new estimates are obtained for the remainder term of the trapezoid and midpoint formula. Applications to some special means are also investigated.

Received: April 18, 2014

AMS Subject Classification: 26D15, 41A55, 41A80, 65C50

Key Words and Phrases: Ostrowski inequality, special means, numerical integration

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DOI: 10.12732/ijpam.v98i2.1 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 98
Issue: 2
Pages: 169 - 180


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