On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space $L_2$
We prove a statement on exact inequalities between the deviations of functions from their linear methods (in the metric of $L_2$) with multipliers defined by a continuous function and majorants determined as the scalar product of the squared modulus of continuity (of order r) in $L_2$ for the lth de...
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| Datum: | 2003 |
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| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3927 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510058856579072 |
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| author | Bozhukha, L. N. Божуха, Л. Н. Божуха, Л. Н. |
| author_facet | Bozhukha, L. N. Божуха, Л. Н. Божуха, Л. Н. |
| author_sort | Bozhukha, L. N. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:15:31Z |
| description | We prove a statement on exact inequalities between the deviations of functions from their linear methods (in the metric of $L_2$) with multipliers defined by a continuous function and majorants determined as the scalar product of the squared modulus of continuity (of order r) in $L_2$ for the lth derivative of the function and a certain weight function θ. We obtain several corollaries of the general theorem. |
| first_indexed | 2026-03-24T02:50:58Z |
| format | Article |
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| id | umjimathkievua-article-3927 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:50:58Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ab/385e81993f0302cff2b93c694a28c7ab.pdf |
| spelling | umjimathkievua-article-39272020-03-18T20:15:31Z On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space $L_2$ О неравенстве типа Джексона при приближении функции линейными методами суммирования в пространстве $L_2$ Bozhukha, L. N. Божуха, Л. Н. Божуха, Л. Н. We prove a statement on exact inequalities between the deviations of functions from their linear methods (in the metric of $L_2$) with multipliers defined by a continuous function and majorants determined as the scalar product of the squared modulus of continuity (of order r) in $L_2$ for the lth derivative of the function and a certain weight function θ. We obtain several corollaries of the general theorem. Встановлено твердження про точні нерівності між відхиленнями функцій від лінійних методів (у метриці $L_2$) 3 мультиплікаторами, визначеними неперервною функцією, і мажорантами, що є скалярним добутком квадрата модуля неперервності (г-го порядку) в $L_2$ 1-і похідної функції і деякої вагової функції θ. Виведено кілька наслідків із загальної теореми. Institute of Mathematics, NAS of Ukraine 2003-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3927 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 4 (2003); 537-545 Український математичний журнал; Том 55 № 4 (2003); 537-545 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3927/4568 https://umj.imath.kiev.ua/index.php/umj/article/view/3927/4569 Copyright (c) 2003 Bozhukha L. N. |
| spellingShingle | Bozhukha, L. N. Божуха, Л. Н. Божуха, Л. Н. On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space $L_2$ |
| title | On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space $L_2$ |
| title_alt | О неравенстве типа Джексона при приближении функции линейными
методами суммирования в пространстве $L_2$ |
| title_full | On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space $L_2$ |
| title_fullStr | On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space $L_2$ |
| title_full_unstemmed | On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space $L_2$ |
| title_short | On a Jackson-Type Inequality in the Approximation of a Function by Linear Summation Methods in the Space $L_2$ |
| title_sort | on a jackson-type inequality in the approximation of a function by linear summation methods in the space $l_2$ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3927 |
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