A remark concerning the modulus of smoothness introduced by Ditzian and Totik
For each functionf(x) continuous on the segment [−1, 1], we set \(\tilde f(t) = f(\cos t)\) . We study the relationship between the ordinarykth modulus of continuity \(\omega _k (\tau ,\tilde f^{(r)} )\) of therth derivative \(\tilde f^{(r)}\) of the function \(\tilde f\) and thekth modul...
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| Datum: | 1995 |
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| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1995
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511788848644096 |
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| author | Dyuzhenkova, O. Yu. Дюженкова, О. Ю. Дюженкова, О. Ю. |
| author_facet | Dyuzhenkova, O. Yu. Дюженкова, О. Ю. Дюженкова, О. Ю. |
| author_sort | Dyuzhenkova, O. Yu. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:13:33Z |
| description | For each functionf(x) continuous on the segment [−1, 1], we set \(\tilde f(t) = f(\cos t)\) . We study the relationship between the ordinarykth modulus of continuity \(\omega _k (\tau ,\tilde f^{(r)} )\) of therth derivative \(\tilde f^{(r)}\) of the function \(\tilde f\) and thekth modulus of continuity \(\bar \omega _{k,r} (\tau ,f^{(r)} )\) with weight ϕ r of the rth derivativef (r) of the functionf introduced by Ditzian and Totik. Thus, ifr is odd andk is even, we prove that these moduli are equivalent ast→0. |
| first_indexed | 2026-03-24T03:18:28Z |
| format | Article |
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| id | umjimathkievua-article-5556 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:18:28Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/41/e65f24ae0491f9f8388e37f84c789c41.pdf |
| spelling | umjimathkievua-article-55562020-03-19T09:13:33Z A remark concerning the modulus of smoothness introduced by Ditzian and Totik Замечание о модуле гладкости 3. Дитзиана и В. Тотика Dyuzhenkova, O. Yu. Дюженкова, О. Ю. Дюженкова, О. Ю. For each functionf(x) continuous on the segment [−1, 1], we set \(\tilde f(t) = f(\cos t)\) . We study the relationship between the ordinarykth modulus of continuity \(\omega _k (\tau ,\tilde f^{(r)} )\) of therth derivative \(\tilde f^{(r)}\) of the function \(\tilde f\) and thekth modulus of continuity \(\bar \omega _{k,r} (\tau ,f^{(r)} )\) with weight ϕ r of the rth derivativef (r) of the functionf introduced by Ditzian and Totik. Thus, ifr is odd andk is even, we prove that these moduli are equivalent ast→0. Для кожної неперервної на $[-1, 1]$ функції $f(x)$ покладемо $\tilde f(t) = f(\cos t)$. Досліджено зв’язок між звичайним 1-м модулем неперервності $\omega _k (\tau ,\tilde f^{(r)} )$ $r$-ї похідної $f(\cos t)$ функції $\tilde f$ та $k$-м модулем неперервності $\bar \omega _{k,r} (\tau ,f^{(r)} )$ з вагою $ϕ_r$ $r$-ї похідної $f^{(r)}$ функції $f$ , що був введений 3. Дітзіаном та В. Тотіко. Institute of Mathematics, NAS of Ukraine 1995-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5556 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 12 (1995); 1627–1638 Український математичний журнал; Том 47 № 12 (1995); 1627–1638 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5556/7800 https://umj.imath.kiev.ua/index.php/umj/article/view/5556/7801 Copyright (c) 1995 Dyuzhenkova O. Yu. |
| spellingShingle | Dyuzhenkova, O. Yu. Дюженкова, О. Ю. Дюженкова, О. Ю. A remark concerning the modulus of smoothness introduced by Ditzian and Totik |
| title | A remark concerning the modulus of smoothness introduced by Ditzian and Totik |
| title_alt | Замечание о модуле гладкости 3. Дитзиана и В. Тотика |
| title_full | A remark concerning the modulus of smoothness introduced by Ditzian and Totik |
| title_fullStr | A remark concerning the modulus of smoothness introduced by Ditzian and Totik |
| title_full_unstemmed | A remark concerning the modulus of smoothness introduced by Ditzian and Totik |
| title_short | A remark concerning the modulus of smoothness introduced by Ditzian and Totik |
| title_sort | remark concerning the modulus of smoothness introduced by ditzian and totik |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5556 |
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