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A SHARP L2 INEQUALITY OF OSTROWSKI TYPE

Part of: Inequalities

Published online by Cambridge University Press:  01 January 2008

ZHENG LIU
ZHENG LIU*
Affiliation:
Institute of Applied Mathematics, School of Science, University of Science and Technology Liaoning, Anshan 114051, Liaoning, China (email: lewzheng@163.net)
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Abstract

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A sharp L2 inequality of Ostrowski type is established, which provides a generalization of some previous results and gives some other interesting results as special cases. Applications in numerical integration are also given.

Keywords

sharp boundOstrowski-type inequalitycorrected trapezoid rulecorrected midpoint rulecorrected Simpson rulecorrected averaged midpoint-trapezoid rule

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 3 , January 2008 , pp. 423 - 429
Copyright
Copyright © Australian Mathematical Society 2008

References

[1]Barnett, N. B., Cerone, P. and Dragomir, S. S., “A sharp bound for the error in the corrected trapezoid rule and applications”, Tamkang J. Math. 33 (2002) 253–258.CrossRefGoogle Scholar
[2]Cerone, P., “On perturbed trapezoidal and midpoint rules”, Korean J. Comput. Appl. Math. 2 (2002) 423–435.CrossRefGoogle Scholar
[3]Pečaric, J. and Franjić, I., “Generalization of corrected Simpson’s formula”, ANZIAM J. 47 (2006) 367–385.CrossRefGoogle Scholar
[4]Ujević, N., “A generalization of the modified Simpson’s rule and error bounds”, ANZIAM J. 47(E) (2005) E1–E13.Google Scholar
[5]Ujević, N. and Roberts, A. J., “A corrected quadrature formula and applications”, ANZIAM J. 45(E) (2004) E41–E56.Google Scholar