Best approximation by «angle» and the absolute Cesàro summability of double Fourier series
This article is devoted to the topic of absolute summation of series or Cesaro summation. The relevance of this article lies in the fact that a type of absolute summation with vector index which has not been previously studied is considered. In this article, a sufficient condition for the vector in...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2023-12-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/605 |
| _version_ | 1827395799075520512 |
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| author | S. Bitimkhan O. Mekesh |
| author_facet | S. Bitimkhan O. Mekesh |
| author_sort | S. Bitimkhan |
| collection | DOAJ |
| description |
This article is devoted to the topic of absolute summation of series or Cesaro summation. The relevance of this article lies in the fact that a type of absolute summation with vector index which has not been previously studied is considered. In this article, a sufficient condition for the vector index absolute summation method was obtained in terms of the best approximation by «angle» of the functions from Lebesgue space. The theorem that gives a sufficient condition proves the conditions that are sufficient in different cases, which may depend on the parameters. From this proved theorem, a sufficient condition on the term mixed smoothness modulus of the function from Lebesgue space, which is easily obtained by a well-known inequality, is also presented.
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| first_indexed | 2024-03-08T18:40:02Z |
| format | Article |
| id | doaj.art-8b13ce7f98674e87ac61096cdd61561c |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:40:02Z |
| publishDate | 2023-12-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-8b13ce7f98674e87ac61096cdd61561c2023-12-29T09:21:05ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112023-12-01112410.31489/2023m4/56-65605Best approximation by «angle» and the absolute Cesàro summability of double Fourier seriesS. BitimkhanO. Mekesh This article is devoted to the topic of absolute summation of series or Cesaro summation. The relevance of this article lies in the fact that a type of absolute summation with vector index which has not been previously studied is considered. In this article, a sufficient condition for the vector index absolute summation method was obtained in terms of the best approximation by «angle» of the functions from Lebesgue space. The theorem that gives a sufficient condition proves the conditions that are sufficient in different cases, which may depend on the parameters. From this proved theorem, a sufficient condition on the term mixed smoothness modulus of the function from Lebesgue space, which is easily obtained by a well-known inequality, is also presented. https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/605trigonometric seriesFourier seriesLebesgue spacebest approximation by «angle»absolute summability of the series |
| spellingShingle | S. Bitimkhan O. Mekesh Best approximation by «angle» and the absolute Cesàro summability of double Fourier series Қарағанды университетінің хабаршысы. Математика сериясы trigonometric series Fourier series Lebesgue space best approximation by «angle» absolute summability of the series |
| title | Best approximation by «angle» and the absolute Cesàro summability of double Fourier series |
| title_full | Best approximation by «angle» and the absolute Cesàro summability of double Fourier series |
| title_fullStr | Best approximation by «angle» and the absolute Cesàro summability of double Fourier series |
| title_full_unstemmed | Best approximation by «angle» and the absolute Cesàro summability of double Fourier series |
| title_short | Best approximation by «angle» and the absolute Cesàro summability of double Fourier series |
| title_sort | best approximation by angle and the absolute cesaro summability of double fourier series |
| topic | trigonometric series Fourier series Lebesgue space best approximation by «angle» absolute summability of the series |
| url | https://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/605 |
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