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Multivariate Fink type identity and multivariate Ostrowski, comparison of means and Grüss type inequalities

✍ Scribed by George A. Anastassiou

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
329 KB
Volume
46
Category
Article
ISSN
0895-7177

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Taylor–Widder representation formulae an
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Based on the very general Taylor-Widder formula, several representation formulae are developed. By applying these are developed very general inequalities of types: Ostrowski, Grüss, comparison of means, Csiszar f -divergence. The estimates involve L p norms, any 1 ≤ p ≤ ∞.

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In this paper we derive some Grüss and Ostrowski-Grüss type inequalities for functions in L p -spaces. As applications, we provide some new estimates for the error in some numerical integration rules. In particular, we deal with the mid-point and trapezoid quadrature rules.