Asymmetric approximations in the space $L_{p(t)}$
We introduce the notion of $(α,β)$-norm in the space $L_{p(t)}$ of functions $x(t)$ for which $$\int\limits_0^1 {\left| {x(t)} \right|^{p(t)}< \infty }$$ where $p(t)$ is a positive measurable function. We establish a criterion for the element of the best $(α,β)$-approximation in the space $L...
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| Datum: | 1999 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1999
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4684 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510842458472448 |
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| author | Litvin, E. G. Polyakov, O. V. Литвин, Е. Г. Поляков, О. В Литвин, Е. Г. Поляков, О. В |
| author_facet | Litvin, E. G. Polyakov, O. V. Литвин, Е. Г. Поляков, О. В Литвин, Е. Г. Поляков, О. В |
| author_sort | Litvin, E. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:11:21Z |
| description | We introduce the notion of $(α,β)$-norm in the space $L_{p(t)}$ of functions $x(t)$ for which
$$\int\limits_0^1 {\left| {x(t)} \right|^{p(t)}< \infty }$$
where $p(t)$ is a positive measurable function. We establish a criterion for the element of the best $(α,β)$-approximation in the space $L_{p(t)}$. We obtain inequalities of the type of duality relations. |
| first_indexed | 2026-03-24T03:03:25Z |
| format | Article |
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| id | umjimathkievua-article-4684 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:03:25Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/79/1fd2c9c501c665a29e7837aa6f9df579.pdf |
| spelling | umjimathkievua-article-46842020-03-18T21:11:21Z Asymmetric approximations in the space $L_{p(t)}$ Несимметричные приближения в пространстве $L_{p(t)}$ Litvin, E. G. Polyakov, O. V. Литвин, Е. Г. Поляков, О. В Литвин, Е. Г. Поляков, О. В We introduce the notion of $(α,β)$-norm in the space $L_{p(t)}$ of functions $x(t)$ for which $$\int\limits_0^1 {\left| {x(t)} \right|^{p(t)}< \infty }$$ where $p(t)$ is a positive measurable function. We establish a criterion for the element of the best $(α,β)$-approximation in the space $L_{p(t)}$. We obtain inequalities of the type of duality relations. Введено поняття про $(α,β)$-норму у просторі $L_{p(t)}$ функцій $x(t)$, для яких $$\int\limits_0^1 {\left| {x(t)} \right|^{p(t)}< \infty }$$ де $p(t)$ — додатна вимірна функція. Встановлено критерій елемента найкращого $(α,β)$-наближення у просторі $L_{p(t)}$. Отримано нерівності типу співвідношень двоїстості. Institute of Mathematics, NAS of Ukraine 1999-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4684 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 7 (1999); 952-959 Український математичний журнал; Том 51 № 7 (1999); 952-959 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4684/6070 https://umj.imath.kiev.ua/index.php/umj/article/view/4684/6071 Copyright (c) 1999 Litvin E. G.; Polyakov O. V. |
| spellingShingle | Litvin, E. G. Polyakov, O. V. Литвин, Е. Г. Поляков, О. В Литвин, Е. Г. Поляков, О. В Asymmetric approximations in the space $L_{p(t)}$ |
| title | Asymmetric approximations in the space $L_{p(t)}$ |
| title_alt | Несимметричные приближения в пространстве $L_{p(t)}$ |
| title_full | Asymmetric approximations in the space $L_{p(t)}$ |
| title_fullStr | Asymmetric approximations in the space $L_{p(t)}$ |
| title_full_unstemmed | Asymmetric approximations in the space $L_{p(t)}$ |
| title_short | Asymmetric approximations in the space $L_{p(t)}$ |
| title_sort | asymmetric approximations in the space $l_{p(t)}$ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4684 |
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