Open Access Research Article

Some Generalized Error Inequalities and Applications

Fiza Zafar1* and NazirAhmad Mir2

Author Affiliations

1 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan

2 Department of Mathematics, COMSATS Institute of Information Technology, Plot no. 30, Sector H-8/1, Islamabad 44000, Pakistan

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Journal of Inequalities and Applications 2008, 2008:845934 doi:10.1155/2008/845934


The electronic version of this article is the complete one and can be found online at: http://www.journalofinequalitiesandapplications.com/content/2008/1/845934


Received:4 February 2008
Revisions received:30 May 2008
Accepted:29 July 2008
Published:21 September 2008

© 2008 The Author(s).

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

We present a family of four-point quadrature rule, a generalization of Gauss-two point, Simpson's , and Lobatto four-point quadrature rule for twice-differentiable mapping. Moreover, it is shown that the corresponding optimal quadrature formula presents better estimate in the context of four-point quadrature formulae of closed type. A unified treatment of error inequalities for different classes of function is also given.

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