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Sharp integral inequalities based on general Euler two-point formulae

Published online by Cambridge University Press:  17 February 2009

J. Pečarić ,
I. Perić  and
A. Vukelić
J. Pečarić
Affiliation:
Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia; e-mail: [email protected].
I. Perić
Affiliation:
Faculty of Food Technology and Biotechnology, Mathematics Department, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia; e-mail: [email protected] and [email protected].
A. Vukelić
Affiliation:
Faculty of Food Technology and Biotechnology, Mathematics Department, University of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia; e-mail: [email protected] and [email protected].
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Abstract

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We consider a family of two-point quadrature formulae, using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation, Lipschitzian functions or R-integrable functions, are proved.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 4 , April 2005 , pp. 555 - 574
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Abramowitz, M. and Stegun, I. A.(eds.), Handbook of mathematical functions with formulae, graphs and mathematical tables, Appl. Math. Series 55 (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]Cerone, P. and Dragomir, S. S., “Trapezoidal type rules from an inequalities point of view”, RGMIA 2 (1999) Article 8.Google Scholar
[4]Cerone, P. C. and Dragomir, S. S., “Midpoint-type rules from an inequalities point of view”, in Handbook of analytic-computational methods in applied mathematics, (Chapman & Hall/CRC, Boca Raton, FL, 2000) 135–200.Google Scholar
[5]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
[6]Dedić, Lj., Matić, M. and Pečarić, J., “On Euler trapezoid formulae”, Appl. Math. Comput. 123 (2001) 37–62.Google Scholar
[7]Dedić, Lj., Matiá, M. and Pečarić, J., “Some inequalities of Euler-Grüss type”, Comput. Math. Appl 41 (2001) 843–856.CrossRefGoogle Scholar
[8]Dedić, Lj., Matić, M. and Pečarić, J., “On Euler midpoint formulae”, ANZIAM J. 46 (2005) 417–438.CrossRefGoogle Scholar
[9]Dragomir, S. S., “A companion of Ostrowski's inequality for functions of bounded variation and applications”, RGMIA 5 (2002) supplement.Google Scholar
[10]Dragomir, S. S., “Some companions of Ostrowski's inequality for absolutely continuous functions and applications”, RGMIA 5 (2002) supplement.Google Scholar
[11]Dragomir, S. S., Cerone, P. and Sofo, A., “Some remarks on the midpoint rule in numerical integration”, Studia Math. Babes-Bolyai Univ. 45 (2000) 63–73.Google Scholar
[12]Dragomir, S. S., Cerone, P. and Sofo, A., “Some remarks on the trapezoid rule in numerical integration”, Indian J. Pure Appl. Math. 31 (2000) 475–494.Google Scholar
[13]Fink, A. M., “Bounds on the deviation of a function from its averages”, Czechoslovak Math. J. 42 (1992) 289–310.CrossRefGoogle Scholar
[14]Guessab, A. and Schmeisser, G., “Sharp integral inequalities of the Hermite-Hadamard type”, J. Approx. Theory 115 (2002) 260–288.Google Scholar
[15]Krylov, V. I., Approximate calculation of integrals (Macmillan, New York-London, 1962).Google Scholar
[16]Matić, M., “Improvement of some inequalities of Euler-Grüss type”, Comput. Math. Appl. 46 (2003) 1325–1336.CrossRefGoogle Scholar
[17]Matić, M., Pearce, C. E. M. and Pečarić, J., “Two-point formulae of Euler type”, ANZLAM J. 44 (2002) 221–245.CrossRefGoogle Scholar