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ANOTHER SHARP L2 INEQUALITY OF OSTROWSKI TYPE

Part of: Inequalities

Published online by Cambridge University Press:  01 July 2008

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

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

Keywords

sharp boundOstrowski type inequalitycorrected Simpson rulecorrected averaged midpoint-trapezoid rulenumerical integration

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 1 , July 2008 , pp. 129 - 136
Copyright
Copyright © Australian Mathematical Society 2009

References

[1]Liu, Z., “Note on a paper by N. Ujević”, Appl. Math. Lett. 20 (2007) 659–663.Google Scholar
[2]Liu, Z., “A sharp L 2 inequality of Ostrowski type”, ANZIAM J. 49 (2008) 423–429.Google Scholar
[3]Pečarić, J. and Franjić, I., “Generalization of corrected Simpson’s formula”, ANZIAM J. 47 (2006) 367–385.Google Scholar
[4]Ujević, N. and Roberts, A. J., “A corrected quadrature formula and applications”, ANZIAM J. 45(E) (2004) E41–E56.Google Scholar
[5]Ujević, N., “A generalization of the modified Simpson’s rule and error bounds”, ANZIAM J. 47(E) (2005) E1–E13.Google Scholar