2017
Том 69
№ 9

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Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions

Pleshakov M. G., Popov P. A.

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Abstract

We consider a 2π-periodic function f continuous on \(\mathbb{R}\) and changing its sign at 2s points y i ∈ [−π, π). For this function, we prove the existence of a trigonometric polynomial T n of degree ≤n that changes its sign at the same points y i and is such that the deviation | f(x) − T n(x) | satisfies the second Jackson inequality.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 1, pp 153-160.

Citation Example: Pleshakov M. G., Popov P. A. Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions // Ukr. Mat. Zh. - 2004. - 56, № 1. - pp. 123-128.

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