Sharp Integral Inequalities of the Hermite–Hadamard Type

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


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
Subjects Historical > FOR Classification > 0102 Applied Mathematics
Historical > FOR Classification > 0103 Numerical and Computational Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords Hermite–Hadamard inequality, two-point quadrature, Lipschitz classes, Lp estimates
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