Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7
Let f ∈ C[0, 1], k = 5, 6, 7. We prove that if f(i/(k − 1)) = 0, i = 0, 1,..., k − 1, then \(\left| {f(x)} \right| \leqslant 2{\text{ }}\mathop {{\text{sup}}}\limits_{x,x + kh \in [0,1]} {\text{ }}\left| {\sum\limits_{j = 0}^k {( - 1)^j } \left( {\mathop {}\limits_j^k } \right)f(x + jh)} \right|.\...
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| Datum: | 2003 |
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| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2003
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510059270766592 |
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| author | Zhelnov, O. D. Желнов, О. Д. |
| author_facet | Zhelnov, O. D. Желнов, О. Д. |
| author_sort | Zhelnov, O. D. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:15:31Z |
| description | Let f ∈ C[0, 1], k = 5, 6, 7. We prove that if f(i/(k − 1)) = 0, i = 0, 1,..., k − 1, then \(\left| {f(x)} \right| \leqslant 2{\text{ }}\mathop {{\text{sup}}}\limits_{x,x + kh \in [0,1]} {\text{ }}\left| {\sum\limits_{j = 0}^k {( - 1)^j } \left( {\mathop {}\limits_j^k } \right)f(x + jh)} \right|.\) |
| first_indexed | 2026-03-24T02:50:58Z |
| format | Article |
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| id | umjimathkievua-article-3928 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
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| language | Ukrainian English |
| last_indexed | 2026-03-24T02:50:58Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/c0/77087fb48d7996183d3fb659ebe01cc0.pdf |
| spelling | umjimathkievua-article-39282020-03-18T20:15:31Z Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7 Інтерполяційні сталі Уітні обмежені двійкою для k = 5, 6, 7 Zhelnov, O. D. Желнов, О. Д. Let f ∈ C[0, 1], k = 5, 6, 7. We prove that if f(i/(k − 1)) = 0, i = 0, 1,..., k − 1, then \(\left| {f(x)} \right| \leqslant 2{\text{ }}\mathop {{\text{sup}}}\limits_{x,x + kh \in [0,1]} {\text{ }}\left| {\sum\limits_{j = 0}^k {( - 1)^j } \left( {\mathop {}\limits_j^k } \right)f(x + jh)} \right|.\) Нехай $f ∈ C[0, 1], k = 5, 6, 7$. Доведено, що якщо $f(i/(k − 1)) = 0, i = 0, 1,..., k − 1$, то $$\left| {f(x)} \right| \leqslant 2{\text{ }}\mathop {{\text{sup}}}\limits_{x,x + kh \in [0,1]} {\text{ }}\left| {\sum\limits_{j = 0}^k {( - 1)^j } \left( {\mathop {}\limits_j^k } \right)f(x + jh)} \right|.$$ Institute of Mathematics, NAS of Ukraine 2003-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3928 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 4 (2003); 546-549 Український математичний журнал; Том 55 № 4 (2003); 546-549 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3928/4570 https://umj.imath.kiev.ua/index.php/umj/article/view/3928/4571 Copyright (c) 2003 Zhelnov O. D. |
| spellingShingle | Zhelnov, O. D. Желнов, О. Д. Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7 |
| title | Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7 |
| title_alt | Інтерполяційні сталі Уітні обмежені двійкою для k = 5, 6, 7 |
| title_full | Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7 |
| title_fullStr | Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7 |
| title_full_unstemmed | Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7 |
| title_short | Whitney Interpolation Constants Bounded by 2 for k = 5, 6, 7 |
| title_sort | whitney interpolation constants bounded by 2 for k = 5, 6, 7 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3928 |
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