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Higher order Ostrowski type inequalities over Euclidean domains. (English) Zbl 1144.26024
The classical Ostrowski inequality for functions on intervals estimates the value of the function minus its average in terms the maximum of its first derivative. In this paper, by using the way of real analysis, this result is extended to functions on general domains using the \(L^\infty\) norm of its nth par derivatives. For radial functions on balls the inequality is sharp.

MSC:
26D15 Inequalities for sums, series and integrals
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[1] Anastassiou, G.A., Ostrowski type inequalities, Proc. amer. math. soc., 123, 3775-3781, (1995) · Zbl 0860.26009
[2] Anastassiou, G.A., Quantitative approximations, (2001), Chapman & Hall/CRC Boca Raton/New York · Zbl 0969.41001
[3] G.A. Anastassiou, J.A. Goldstein, Ostrowski type inequalities over Euclidean domains, Atti Accad. Naz. Lincei, in press · Zbl 1142.26011
[4] Evans, L.C., Partial differential equations, Grad. stud. math., vol. 19, (1998), Amer. Math. Soc. Providence, RI
[5] Ostrowski, A., Über die absolutabweichung einer differentiebaren funktion von ihrem integralmittelwert, Comment. math. helv., 10, 226-227, (1938) · JFM 64.0209.01
[6] Pitman, J., Probability, (1993), Springer-Verlag New York · Zbl 0779.60001
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