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• 1 International Mathematical Center of NAS of Ukraine 01601 Tereschenkivs’ka str., 3 Kyiv Ukraine
• | 2 Toulon University and Centre de Physique Théorique, CNRS — Luminy, Case 907 13288 Marseille Cedex 09 France
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Abstract

Let f be a real continuous 2π-periodic function changing its sign in the fixed distinct points yiY:= {yi}i∈ℤ such that for x ∈ [yi, yi−1], f(x) ≧ 0 if i is odd and f(x) ≦ 0 if i is even. Then for each nN(Y) we construct a trigonometric polynomial Pn of order ≦ n, changing its sign at the same points yiY as f, and

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left\| {f - P_n } \right\| \leqq c(s)\omega _3 \left( {f,\frac{\pi } {n}} \right),$$ \end{document}
where N(Y) is a constant depending only on Y, c(s) is a constant depending only on s, ω3(f, t) is the third modulus of smoothness of f and ∥ · ∥ is the max-norm.

Acta Mathematica Hungarica
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• Impact Factor (2019): 0.588
• Scimago Journal Rank (2019): 0.489
• SJR Hirsch-Index (2019): 38
• SJR Quartile Score (2019): Q2 Mathematics (miscellaneous)
• Impact Factor (2018): 0.538
• Scimago Journal Rank (2018): 0.488
• SJR Hirsch-Index (2018): 36
• SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
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H-1051 Budapest, Hungary, Széchenyi István tér 9.
Springer Nature Switzerland AG
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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