Some new Cesàro sequence spaces of order $\alpha$
UDC 517.98 We introduce the spaces $\ell_\infty(C_\alpha),$ $f(C_\alpha),$ and $f_0(C_\alpha)$ of Ces\`{a}ro bounded, Ces\`{a}ro almost convergent, and Ces\`{a}ro almost null sequences of order $\alpha,$ respectively. Moreover, we establish some inclusion relations for these spaces and determine the...
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| Date: | 2024 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7333 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512654200668160 |
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| author | Savaşcı, Medine Yeşilkayagil Başar, Feyzi Savaşcı, Medine Yeşilkayagil Başar, Feyzi |
| author_facet | Savaşcı, Medine Yeşilkayagil Başar, Feyzi Savaşcı, Medine Yeşilkayagil Başar, Feyzi |
| author_sort | Savaşcı, Medine Yeşilkayagil |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:35:18Z |
| description | UDC 517.98
We introduce the spaces $\ell_\infty(C_\alpha),$ $f(C_\alpha),$ and $f_0(C_\alpha)$ of Ces\`{a}ro bounded, Ces\`{a}ro almost convergent, and Ces\`{a}ro almost null sequences of order $\alpha,$ respectively. Moreover, we establish some inclusion relations for these spaces and determine the $\alpha$-, $\beta$- and $\gamma$-duals of the spaces  $\ell_\infty(C_\alpha)$ and $f(C_\alpha).$  Finally, we characterize the classes of matrix transformations from the space $f(C_\alpha)$ to any sequence space $Y$ and from any sequence space $Y$ to the space $f(C_\alpha).$ |
| doi_str_mv | 10.3842/umzh.v76i3.7333 |
| first_indexed | 2026-03-24T03:32:13Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7333 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:13Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-73332024-06-19T00:35:18Z Some new Cesàro sequence spaces of order $\alpha$ Some new Cesàro sequence spaces of order $\alpha$ Savaşcı, Medine Yeşilkayagil Başar, Feyzi Savaşcı, Medine Yeşilkayagil Başar, Feyzi Normed sequence space, $\alpha$-, $\beta$- and $\gamma$-duals and matrix mappings UDC 517.98 We introduce the spaces $\ell_\infty(C_\alpha),$ $f(C_\alpha),$ and $f_0(C_\alpha)$ of Ces\`{a}ro bounded, Ces\`{a}ro almost convergent, and Ces\`{a}ro almost null sequences of order $\alpha,$ respectively. Moreover, we establish some inclusion relations for these spaces and determine the $\alpha$-, $\beta$- and $\gamma$-duals of the spaces  $\ell_\infty(C_\alpha)$ and $f(C_\alpha).$  Finally, we characterize the classes of matrix transformations from the space $f(C_\alpha)$ to any sequence space $Y$ and from any sequence space $Y$ to the space $f(C_\alpha).$ УДК 517.98 Деякі нові простори послідовностей Чезаро порядку $\alpha$ Введено простори $\ell_\infty(C_\alpha),$ $f(C_\alpha)$ і $f_0(C_\alpha)$ Чезаро обмежених, Чезаро майже збіжних і Чезаро майже нульових послідовностей порядку $\alpha$ відповідно. Крім того,  встановлено деякі співвідношення включення для  цих просторів і визначено $\alpha$-, $\beta$- та $\gamma$-дуальні простори для $\ell_\infty(C_\alpha)$ та $f(C_\alpha).$ Насамкінець охарактеризовано класи матричних перетворень з простору $f(C_\alpha)$ в довільний простір  послідовностей $Y$ та з  довільного простору послідовностей $Y$ у простір $f(C_\alpha).$  Institute of Mathematics, NAS of Ukraine 2024-03-25 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7333 10.3842/umzh.v76i3.7333 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 3 (2024); 432 - 446 Український математичний журнал; Том 76 № 3 (2024); 432 - 446 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7333/9862 Copyright (c) 2024 Feyzi Başar |
| spellingShingle | Savaşcı, Medine Yeşilkayagil Başar, Feyzi Savaşcı, Medine Yeşilkayagil Başar, Feyzi Some new Cesàro sequence spaces of order $\alpha$ |
| title | Some new Cesàro sequence spaces of order $\alpha$ |
| title_alt | Some new Cesàro sequence spaces of order $\alpha$ |
| title_full | Some new Cesàro sequence spaces of order $\alpha$ |
| title_fullStr | Some new Cesàro sequence spaces of order $\alpha$ |
| title_full_unstemmed | Some new Cesàro sequence spaces of order $\alpha$ |
| title_short | Some new Cesàro sequence spaces of order $\alpha$ |
| title_sort | some new cesàro sequence spaces of order $\alpha$ |
| topic_facet | Normed sequence space $\alpha$- $\beta$- and $\gamma$-duals and matrix mappings |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7333 |
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