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

Trudy Inst. Mat. i Mekh. UrO RAN, 2010 Volume 16, Number 4, Pages 246–253 (Mi timm658)

This article is cited in 2 papers

On the Jackson–Stechkin inequality for algebraic polynomials

A. V. Mironenko

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

Abstract: The Jackson–Stechkin inequality is considered, which estimates the value of the best uniform approximation of a continuous function by algebraic polynomials on a closed interval in terms of values of the modulus of continuity of the approximated function. A variant of the inequality with second-order modulus of continuity and explicit specification of the argument of the modulus of continuity and the constant is proved.

Keywords: Jackson inequality, approximation by algebraic polynomials, modulus of continuity.

UDC: 517.518.82

Received: 01.05.2010


 English version:
Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2011, 273, suppl. 1, S116–S123

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