Coconvex approximation of periodic functions
The Jackson inequality E n (f ) ≤ c ω 3 (f , π / n ) connects the value of the best uniform approximation E n (f ) of a 2π-periodic function f : R → R by trigonometric polynomials of order ≤ n — 1 with its third modulus...
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| Datum: | 2007 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2007
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3290 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | The Jackson inequality E n (f ) ≤ c ω 3 (f , π / n )
connects the value of the best uniform approximation E n (f ) of a 2π-periodic
function f : R → R by trigonometric polynomials of order ≤ n — 1 with its third modulus
of continuity ω 3 (f, t ).
In the present paper, we show that this inequality is true if continuous 2π-periodic functions that change their convexity
on [—π, π) only at every point of a fixed finite set consisting of the even number of points are approximated by polynomials coconvex to them. |
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