Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight
UDC 517.5 We introduce a new class of functions, namely, the generalized Zygmund class with weight. Moreover, we determine the degree of approximation for functions belonging to this class. The degree of approximation is expressed in terms of two moduli of continuity of the second order $w_1$ and $...
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| Date: | 2025 |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7670 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512697083232256 |
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| author | Krasniqi, Xhevat Z. Krasniqi, Xhevat Z. |
| author_facet | Krasniqi, Xhevat Z. Krasniqi, Xhevat Z. |
| author_sort | Krasniqi, Xhevat Z. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-11-08T09:36:24Z |
| description | UDC 517.5
We introduce a new class of functions, namely, the generalized Zygmund class with weight. Moreover, we determine the degree of approximation for functions belonging to this class. The degree of approximation is expressed in terms of two moduli of continuity of the second order $w_1$ and $w_2$ such that $w_1/w_2$ is positive and nondecreasing. To realize this task, for approximation we use the even-type delayed mean of their Fourier series. |
| doi_str_mv | 10.3842/umzh.v77i3.7670 |
| first_indexed | 2026-03-24T03:32:54Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7670 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:54Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-76702025-11-08T09:36:24Z Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight Krasniqi, Xhevat Z. Krasniqi, Xhevat Z. Degree of approximation, Fourier series, Zygmund class with weight, modulus of continuity, even-delayed mean. UDC 517.5 We introduce a new class of functions, namely, the generalized Zygmund class with weight. Moreover, we determine the degree of approximation for functions belonging to this class. The degree of approximation is expressed in terms of two moduli of continuity of the second order $w_1$ and $w_2$ such that $w_1/w_2$ is positive and nondecreasing. To realize this task, for approximation we use the even-type delayed mean of their Fourier series. УДК 517.5 Застoсування запізнілого середнього парного типу для апроксимації функцій із узагальненого класу Зиґмунда з вагою Уведено новий клас функцій – узагальнений клас Зиґмунда з вагою. До того ж визначено степінь наближення для функцій, що належать до цього класу. Степінь наближення виражено через два модулі неперервності другого порядку $w_1$ і $w_2$ таким чином, що $w_1/w_2$ є додатними й неспадними. Щоб досягти цієї мети, для апроксимації використано парне запізніле середнє їхніх рядів Фур'є. Institute of Mathematics, NAS of Ukraine 2025-11-07 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7670 10.3842/umzh.v77i3.7670 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 3 (2025); 233 Український математичний журнал; Том 77 № 3 (2025); 233 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7670/10421 Copyright (c) 2025 Xhevat Z. Krasniqi |
| spellingShingle | Krasniqi, Xhevat Z. Krasniqi, Xhevat Z. Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight |
| title | Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight |
| title_alt | Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight |
| title_full | Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight |
| title_fullStr | Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight |
| title_full_unstemmed | Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight |
| title_short | Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight |
| title_sort | application of the even-type delayed mean in the approximation of functions from the generalized zygmund class with weight |
| topic_facet | Degree of approximation Fourier series Zygmund class with weight modulus of continuity even-delayed mean. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7670 |
| work_keys_str_mv | AT krasniqixhevatz applicationoftheeventypedelayedmeanintheapproximationoffunctionsfromthegeneralizedzygmundclasswithweight AT krasniqixhevatz applicationoftheeventypedelayedmeanintheapproximationoffunctionsfromthegeneralizedzygmundclasswithweight |