Open Access

Some Generalized Error Inequalities and Applications

Journal of Inequalities and Applications20082008:845934

https://doi.org/10.1155/2008/845934

Received: 4 February 2008

Accepted: 29 July 2008

Published: 21 September 2008

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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Authors’ Affiliations

(1)
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University
(2)
Department of Mathematics, COMSATS Institute of Information Technology

Copyright

© F. Zafar and N. A. Mir. 2008

This article is published under license to BioMed Central Ltd. 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.