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Sharp Integral Inequalities of the Hermite–Hadamard Type

Guessab, Allal and Schmeisser, Gerhard (1998) Sharp Integral Inequalities of the Hermite–Hadamard Type. RGMIA research report collection, 5 (Supp).

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Abstract

We consider a family of two-point quadrature formulae and establish a sharp estimates for the remainders under various regularity conditions. Improved forms of certain integral inequalities due to hermite-Hadamard, Iyengar, Milovanović-Pecaric, and others are obtained as special cases. Our results may also be interpreted as analogues to a theorem of Ostrowski on the deviation of a functions from its averages.

Item Type: Article
Uncontrolled Keywords: Hermite–Hadamard inequality, two-point quadrature, Lipschitz classes, Lp estimates
Subjects: FOR Classification > 0102 Applied Mathematics
FOR Classification > 0103 Numerical and Computational Mathematics
Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Depositing User: Research Group in Mathematical Inequalities and Applications
Date Deposited: 19 Jul 2012 01:03
Last Modified: 23 May 2013 16:54
URI: http://vuir.vu.edu.au/id/eprint/18075
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