The ANZIAM Journal

  • The ANZIAM Journal (2009), 51 : pp 67-101
  • Copyright © Australian Mathematical Society 2010
  • DOI: 10.1017/S1446181109000315 (About DOI)
  • Published online: 09 March 2010

Table of Contents - 2009 - Volume 51, Issue 01  

Cambridge Journals Online - CUP Full-Text Page
The ANZIAM Journal (2009), 51:67-101 Cambridge University Press
Copyright © Australian Mathematical Society 2010
doi:10.1017/S1446181109000315

Research Article

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

A. AGLIĆ ALJINOVIĆa1 c1, J. PEČARIĆa2 and M. RIBIČIĆ PENAVAa3

a1 Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10 000 Zagreb, Croatia (email: andrea.aglic@fer.hr)
a2 Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10 000 Zagreb, Croatia (email: pecaric@hazu.hr)
a3 Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31 000 Osijek, Croatia (email: mihaela@mathos.hr)
Article author query
aglić aljinović a [Google Scholar]
pečarić j [Google Scholar]
ribičić penava m [Google Scholar]

Abstract

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.

(Received July 13 2007)

(Revised July 27 2009)

2000 Mathematics subject classificationprimary 26D15; secondary 26D20; 41A55

Keywords and phrasesTaylor’s formula; Montgomery’s identity; two-point formulae; Bullen-type inequalities

Correspondence:

c1 For correspondence; e-mail: andrea.aglic@fer.hr

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