Pointwise estimation of comonotone approximation
We prove that, for a continuous function f(x) defined on the interval [−1,1] and having finitely many intervals where it is either nonincreasing or nondecreasing, one can always find a sequence of polynomials P n (x) with the same local properties of monotonicity as the function f(x) and such that...
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| Дата: | 1994 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1994
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5585 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511816710356992 |
|---|---|
| author | Dzyubenko, H. A. Дзюбенко, Г. А. |
| author_facet | Dzyubenko, H. A. Дзюбенко, Г. А. |
| author_sort | Dzyubenko, H. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:14:13Z |
| description | We prove that, for a continuous function f(x) defined on the interval [−1,1] and having finitely many intervals where it is either nonincreasing or nondecreasing, one can always find a sequence of polynomials P n (x) with the same local properties of monotonicity as the function f(x) and such that ¦f(x)−P n (x) ¦≤Cω2(f;n−2+n −1√1−x 2), whereC is a constant that depends on the length of the smallest interval. |
| first_indexed | 2026-03-24T03:18:54Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5585 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:18:54Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/3f/9cdad75844fbd5f0abeb8b369e7e823f.pdf |
| spelling | umjimathkievua-article-55852020-03-19T09:14:13Z Pointwise estimation of comonotone approximation Поточечная оценка комонотонного приближения Dzyubenko, H. A. Дзюбенко, Г. А. We prove that, for a continuous function f(x) defined on the interval [−1,1] and having finitely many intervals where it is either nonincreasing or nondecreasing, one can always find a sequence of polynomials P n (x) with the same local properties of monotonicity as the function f(x) and such that ¦f(x)−P n (x) ¦≤Cω2(f;n−2+n −1√1−x 2), whereC is a constant that depends on the length of the smallest interval. Доведено, що для неперервної на [- 1; 1 ] функції $f(x)$ з обмеженою кількістю проміжків незростання і неспадання існує послідовність многочленів $P_n (x)$, локально монотонних так само, як $f(x)$ і $|f(x) − P_n (x) | ≤C ω_2(f;n^{−2} + n^{−1}\sqrt(1−x^2)$ , $C$ — стала, яка залежить від довжини найменшого проміжку. Institute of Mathematics, NAS of Ukraine 1994-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5585 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 11 (1994); 1467–1472 Український математичний журнал; Том 46 № 11 (1994); 1467–1472 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5585/7855 https://umj.imath.kiev.ua/index.php/umj/article/view/5585/7856 Copyright (c) 1994 Dzyubenko H. A. |
| spellingShingle | Dzyubenko, H. A. Дзюбенко, Г. А. Pointwise estimation of comonotone approximation |
| title | Pointwise estimation of comonotone approximation |
| title_alt | Поточечная оценка комонотонного приближения |
| title_full | Pointwise estimation of comonotone approximation |
| title_fullStr | Pointwise estimation of comonotone approximation |
| title_full_unstemmed | Pointwise estimation of comonotone approximation |
| title_short | Pointwise estimation of comonotone approximation |
| title_sort | pointwise estimation of comonotone approximation |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5585 |
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