Ostrowski type inequalities
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- by George A. Anastassiou PDF
- Proc. Amer. Math. Soc. 123 (1995), 3775-3781 Request permission
Abstract:
Optimal upper bounds are given to the deviation of a function $f \in {C^N}([a,b]),N \in \mathbb {N}$, from its averages. These bounds are of the form $A \bullet {\left \| {{f^{(N)}}} \right \|_\infty }$, where A is the smallest universal constant, i.e., the produced inequalities are sharp and sometimes are attained. This work has been greatly motivated by the works of Ostrowski (1938) and Fink (1992).References
- A. M. Fink, Bounds on the deviation of a function from its averages, Czechoslovak Math. J. 42(117) (1992), no. 2, 289–310. MR 1179500
- Alexander Ostrowski, Über die Absolutabweichung einer differentiierbaren Funktion von ihrem Integralmittelwert, Comment. Math. Helv. 10 (1937), no. 1, 226–227 (German). MR 1509574, DOI 10.1007/BF01214290
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3775-3781
- MSC: Primary 26D10; Secondary 26A99, 41A44
- DOI: https://doi.org/10.1090/S0002-9939-1995-1283537-3
- MathSciNet review: 1283537