Improved version of perturbed Ostrowski type inequalities for \(n\)-times differentiable mappings with three-step kernel and its application

Volume 9, Issue 5, pp 3319--3332 http://dx.doi.org/10.22436/jnsa.009.05.118

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Authors

A. R. Kashif - Department of Mathematics, Capital University of Sciences and Technology, Islamabad, Pakistan. M. Shoaib - Abu Dhabi Mens College, Higher Colleges of Technology, P. O. Box 25035, Abu Dhabi, United Arab Emirates. M. A. Latif - School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa.

Abstract

New integral inequalities of Ostrowski type are developed for n-times differentiable mappings by using a 3-step kernel when either \(f^{(n)} \in L^1[a; b]\) or \(f \in L^2[a; b]\). Some new inequalities are derived as special cases of the obtained inequalities. New efficient quadrature rules are also derived with the help of obtained inequalities. The efficiency of the new quadrature rules is demonstrated with the help of specific examples. Finally, applications for cumulative distribution functions is also provided.

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Keywords

• Ostrowski inequality
• Čebyšev-Grüss inequality
• Čebyšev functional.

MSC

•  26D07
•  26D10
•  26D15

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