Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions
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...
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| Date: | 2004 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3734 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509865584099328 |
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| author | Pleshakov, M. G. Popov, P. A. Плешаков, М. Г. Попов, П. А. Плешаков, М. Г. Попов, П. А. |
| author_facet | Pleshakov, M. G. Popov, P. A. Плешаков, М. Г. Попов, П. А. Плешаков, М. Г. Попов, П. А. |
| author_sort | Pleshakov, M. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:05:58Z |
| description | 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. |
| first_indexed | 2026-03-24T02:47:54Z |
| format | Article |
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| id | umjimathkievua-article-3734 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:47:54Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/23/ea9eae7243cf964c44f61fd9eafa0e23.pdf |
| spelling | umjimathkievua-article-37342020-03-18T20:05:58Z Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions Второе неравенство Джексона в знакосохраняющем приближении периодических функций Pleshakov, M. G. Popov, P. A. Плешаков, М. Г. Попов, П. А. Плешаков, М. Г. Попов, П. А. 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. Для 2π-періодичної неперервної на \(\mathbb{R}\) функції, що змінює знак у $2s$ точках y i ∈ [−π, π), доведено існування тригопометричного полінома $T_n$ порядку $≤n$, який змінює знак у тих самих точках $y_i$ і такий, що для відхилення $| f(x) − T_n(x) |$ має місце друга нерівність Джексона. Institute of Mathematics, NAS of Ukraine 2004-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3734 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 1 (2004); 123-128 Український математичний журнал; Том 56 № 1 (2004); 123-128 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3734/4192 https://umj.imath.kiev.ua/index.php/umj/article/view/3734/4193 Copyright (c) 2004 Pleshakov M. G.; Popov P. A. |
| spellingShingle | Pleshakov, M. G. Popov, P. A. Плешаков, М. Г. Попов, П. А. Плешаков, М. Г. Попов, П. А. Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions |
| title | Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions |
| title_alt | Второе неравенство Джексона в знакосохраняющем
приближении периодических функций |
| title_full | Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions |
| title_fullStr | Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions |
| title_full_unstemmed | Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions |
| title_short | Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions |
| title_sort | second jackson inequality in a sign-preserving approximation of periodic functions |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3734 |
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