On the paranormed binomial sequence spaces
In this paper the sequence spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, $b_{\infty}^{r,s}(p)$ and $b^{r,s}(p)$ which are the generalization of the classical Maddox's paranormed sequence spaces have been introduced and proved that the spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, $b_{\infty}^{r,s}(p)$ and $b...
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| Format: | Article |
| Language: | English |
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Emrah Evren KARA
2018-09-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/542396 |
| _version_ | 1797350240351682560 |
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| author | Ali Köseoğlu Serkan Demiriz Hacer Bilgin Ellidokuzoğlu |
| author_facet | Ali Köseoğlu Serkan Demiriz Hacer Bilgin Ellidokuzoğlu |
| author_sort | Ali Köseoğlu |
| collection | DOAJ |
| description | In this paper the sequence spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, $b_{\infty}^{r,s}(p)$ and $b^{r,s}(p)$ which are the generalization of the classical Maddox's paranormed sequence spaces have been introduced and proved that the spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, $b_{\infty}^{r,s}(p)$ and $b^{r,s}(p)$ are linearly isomorphic to spaces $c_0(p)$, $c(p)$, $\ell_{\infty}(p)$ and $\ell(p)$, respectively. Besides this, the $\alpha-,\beta-$ and $\gamma-$duals of the spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, and $b^{r,s}(p)$ have been computed, their bases have been constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices $(b_0^{r,s}(p) : \mu)$, $(b^{r,s}_c(p): \mu)$ and $(b^{r,s}(p): \mu)$ have been characterized, where $\mu$ is one of the sequence spaces $\ell_\infty,c$ and $c_0$ and derives the other characterizations for the special cases of $\mu$. |
| first_indexed | 2024-03-08T12:41:51Z |
| format | Article |
| id | doaj.art-f1d90f367ffb4cfd89964ce0cb8ba94d |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:41:51Z |
| publishDate | 2018-09-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-f1d90f367ffb4cfd89964ce0cb8ba94d2024-01-21T11:14:36ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532018-09-011313714710.32323/ujma.3952471225On the paranormed binomial sequence spacesAli KöseoğluSerkan DemirizHacer Bilgin EllidokuzoğluIn this paper the sequence spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, $b_{\infty}^{r,s}(p)$ and $b^{r,s}(p)$ which are the generalization of the classical Maddox's paranormed sequence spaces have been introduced and proved that the spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, $b_{\infty}^{r,s}(p)$ and $b^{r,s}(p)$ are linearly isomorphic to spaces $c_0(p)$, $c(p)$, $\ell_{\infty}(p)$ and $\ell(p)$, respectively. Besides this, the $\alpha-,\beta-$ and $\gamma-$duals of the spaces $b_0^{r,s}(p)$, $b_c^{r,s}(p)$, and $b^{r,s}(p)$ have been computed, their bases have been constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices $(b_0^{r,s}(p) : \mu)$, $(b^{r,s}_c(p): \mu)$ and $(b^{r,s}(p): \mu)$ have been characterized, where $\mu$ is one of the sequence spaces $\ell_\infty,c$ and $c_0$ and derives the other characterizations for the special cases of $\mu$.https://dergipark.org.tr/tr/download/article-file/542396binomial sequence spacesparanormmatrix domainmatrix transformations |
| spellingShingle | Ali Köseoğlu Serkan Demiriz Hacer Bilgin Ellidokuzoğlu On the paranormed binomial sequence spaces Universal Journal of Mathematics and Applications binomial sequence spaces paranorm matrix domain matrix transformations |
| title | On the paranormed binomial sequence spaces |
| title_full | On the paranormed binomial sequence spaces |
| title_fullStr | On the paranormed binomial sequence spaces |
| title_full_unstemmed | On the paranormed binomial sequence spaces |
| title_short | On the paranormed binomial sequence spaces |
| title_sort | on the paranormed binomial sequence spaces |
| topic | binomial sequence spaces paranorm matrix domain matrix transformations |
| url | https://dergipark.org.tr/tr/download/article-file/542396 |
| work_keys_str_mv | AT alikoseoglu ontheparanormedbinomialsequencespaces AT serkandemiriz ontheparanormedbinomialsequencespaces AT hacerbilginellidokuzoglu ontheparanormedbinomialsequencespaces |