Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 845934, 15 pages
doi:10.1155/2008/845934
Research Article

Some Generalized Error Inequalities and Applications

Fiza Zafar1 and Nazir Ahmad Mir2

 1Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
2Department of Mathematics, COMSATS Institute of Information Technology, Plot no. 30, Sector H-8/1, Islamabad 44000, Pakistan
Received 4 February 2008; Revised 30 May 2008; Accepted 29 July 2008

Recommended by Sever Dragomir

Abstract

We present a family of four-point quadrature rule, a generalization of Gauss-two point, Simpson's 3/8, 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.