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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ostrowski type inequalities


Author: George A. Anastassiou
Journal: Proc. Amer. Math. Soc. 123 (1995), 3775-3781
MSC: Primary 26D10; Secondary 26A99, 41A44
MathSciNet review: 1283537
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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\Vert {{f^{(N)}}} \right\Vert _\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).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1283537-3
PII: S 0002-9939(1995)1283537-3
Keywords: Function average, deviation of a function, best constant, sharp/attained inequality
Article copyright: © Copyright 1995 American Mathematical Society