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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Keywords: Function average, deviation of a function, best constant, sharp/attained inequality
Article copyright: © Copyright 1995 American Mathematical Society