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SHARP INTEGRAL INEQUALITIES BASED ON GENERAL TWO-POINT FORMULAE VIA AN EXTENSION OF MONTGOMERY’S IDENTITY

Part of: Inequalities Approximations and expansions

Published online by Cambridge University Press:  09 March 2010

A. AGLIĆ ALJINOVIĆ ,
J. PEČARIĆ  and
M. RIBIČIĆ PENAVA
A. AGLIĆ ALJINOVIĆ*
Affiliation:
Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10 000 Zagreb, Croatia (email: [email protected])
J. PEČARIĆ
Affiliation:
Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10 000 Zagreb, Croatia (email: [email protected])
M. RIBIČIĆ PENAVA
Affiliation:
Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31 000 Osijek, Croatia (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We consider families of general two-point quadrature formulae, using the extension of Montgomery’s identity via Taylor’s formula. The formulae obtained are used to present a number of inequalities for functions whose derivatives are from Lp spaces and Bullen-type inequalities.

Keywords

Taylor’s formulaMontgomery’s identitytwo-point formulaeBullen-type inequalities

MSC classification

Secondary: 26D15: Inequalities for sums, series and integrals 41A55: Approximate quadratures
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 1 , July 2009 , pp. 67 - 101
Copyright
Copyright © Australian Mathematical Society 2010

References

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