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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2008 Volume 14, Number 3, Pages 145–152 (Mi timm48)

This article is cited in 1 paper

On the estimate of the uniform deviation from the class of functions with bounded third derivative

A. V. Mironenko

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The problem of the uniform approximation of a continuous function on a closed interval by a class of functions with a uniformly bounded third derivative is considered. It is shown that the value of best approximation of a function by this class cannot be estimated linearly in terms of its third-order modulus of continuity. At the same time, such estimates exist for classes with bounded first or second derivatives.

UDC: 517.518.2

Received: 29.02.2008


 English version:
Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2009, 264, suppl. 1, S168–S176

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