On Exact Estimates for the Pointwise Approximation of the Classes $W^rH^ω$ by Algebraic Polynomials
We obtain estimates for the approximation of functions of the class W r H ω, where ω(t) is a convex modulus of continuity such that tω′(t) does not decrease, by algebraic polynomials with regard for the position of a point on the segment [−1, 1]. The estimates obtained cannot be improved for all mod...
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| Datum: | 2001 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4299 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510430952161280 |
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| author | Motornyi, V. P. Моторный, В. П. Моторный, В. П. |
| author_facet | Motornyi, V. P. Моторный, В. П. Моторный, В. П. |
| author_sort | Motornyi, V. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:59Z |
| description | We obtain estimates for the approximation of functions of the class W r H ω, where ω(t) is a convex modulus of continuity such that tω′(t) does not decrease, by algebraic polynomials with regard for the position of a point on the segment [−1, 1]. The estimates obtained cannot be improved for all moduli of continuity simultaneously. |
| first_indexed | 2026-03-24T02:56:53Z |
| format | Article |
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| id | umjimathkievua-article-4299 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:56:53Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/1d/92e1af687093f09ebe91289ae2f1fa1d.pdf |
| spelling | umjimathkievua-article-42992020-03-18T20:25:59Z On Exact Estimates for the Pointwise Approximation of the Classes $W^rH^ω$ by Algebraic Polynomials О точных оценках поточечного приближения алгебраическими многочленами классов $W^rH^ω$ Motornyi, V. P. Моторный, В. П. Моторный, В. П. We obtain estimates for the approximation of functions of the class W r H ω, where ω(t) is a convex modulus of continuity such that tω′(t) does not decrease, by algebraic polynomials with regard for the position of a point on the segment [−1, 1]. The estimates obtained cannot be improved for all moduli of continuity simultaneously. Одержано оцінки наближення функцій класу $W^rH^ω$ ($ω(t)$ — опуклий модуль неперервності, такий, що $tω′(t)$ не спадає) алгебраїчними многочленами з урахуванням положення точки на відрізку $[— 1, 1]$, які неможливо покращити одночасно для всіх модулів неперервності. Institute of Mathematics, NAS of Ukraine 2001-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4299 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 6 (2001); 783-799 Український математичний журнал; Том 53 № 6 (2001); 783-799 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4299/5302 https://umj.imath.kiev.ua/index.php/umj/article/view/4299/5303 Copyright (c) 2001 Motornyi V. P. |
| spellingShingle | Motornyi, V. P. Моторный, В. П. Моторный, В. П. On Exact Estimates for the Pointwise Approximation of the Classes $W^rH^ω$ by Algebraic Polynomials |
| title | On Exact Estimates for the Pointwise Approximation of the Classes $W^rH^ω$ by Algebraic Polynomials |
| title_alt | О точных оценках поточечного приближения алгебраическими многочленами классов $W^rH^ω$ |
| title_full | On Exact Estimates for the Pointwise Approximation of the Classes $W^rH^ω$ by Algebraic Polynomials |
| title_fullStr | On Exact Estimates for the Pointwise Approximation of the Classes $W^rH^ω$ by Algebraic Polynomials |
| title_full_unstemmed | On Exact Estimates for the Pointwise Approximation of the Classes $W^rH^ω$ by Algebraic Polynomials |
| title_short | On Exact Estimates for the Pointwise Approximation of the Classes $W^rH^ω$ by Algebraic Polynomials |
| title_sort | on exact estimates for the pointwise approximation of the classes $w^rh^ω$ by algebraic polynomials |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4299 |
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