Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-12T22:41:30.093Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalisation of a corrected Simpson's formula

Published online by Cambridge University Press:  17 February 2009

J. Pečarić  and
I. Franjić
J. Pečarić
Affiliation:
Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia; e-mail: pecaric@mahazu.hazu.hr.
I. Franjić
Affiliation:
Faculty of Food Technology and Biotechnology, Mathematics department, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia; e-mail: ifranjic@pbf.hr.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The results obtained by A. J. Roberts and N. Ujević in a recent paper are generalised. A number of inequalities for functions whose derivatives are either functions of bounded variation or Lipschitzian functions or R-integrable functions are derived. Also, some error estimates for the derived formulae are obtained.

Keywords

three-point quadrature formulaecorrected Simpson's formulafunctions of bounded variationLipschitzian functions.
Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 3 , January 2006 , pp. 367 - 385
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Abramowitz, M. and Stegun, I. A. (eds.), Hazdbook of mathematical functions with formulae, graphs and mathematical tables, Appl. Math. Ser. 55, 4th printing (National Bureau of Standards, Washington, 1965).Google Scholar
[2]Berezin, I. S. and Zhidkov, N. P., Computing methods Vol. 1 (Pergamon Press, Oxford, 1965).Google Scholar
[3]Dedić, Lj., Matić, M. and Pečarić, J., “On generalizations of Ostrowski inequality via some Euler-type identities”, Math. Inequal. Appl. 3 (2000) 337–353.Google Scholar
[4]Dedić, Lj., Matić, M. and Pečarić, J., “Some inequalities of Euler-Grüss type”, Comput. Math. Appl. 41 (2001) 843–856.Google Scholar
[5]Krylov, V. I., Approximate calculation of integrals (Macmillan, New York, 1962).Google Scholar
[6]Matić, M., “Improvement of some inequalities of Euler-Grüss type”, Comput. Math. Appl. 46(2003) 1325–1336.Google Scholar
[7]Ujević, N. and Roberts, A. J., “A corrected quadrature formula and applications”, ANZIAM J. 45(E) (2004) E41–E56.CrossRefGoogle Scholar