The binomial sequence spaces of nonabsolute type
Abstract In this paper, we introduce the binomial sequence spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ of nonabsolute type which include the spaces c 0 $c_{0}$ and c, respectively. Also, we prove that the spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ are linearly isomorph...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2016-11-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1256-0 |
| _version_ | 1811229404145123328 |
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| author | Mustafa Cemil Bişgin |
| author_facet | Mustafa Cemil Bişgin |
| author_sort | Mustafa Cemil Bişgin |
| collection | DOAJ |
| description | Abstract In this paper, we introduce the binomial sequence spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ of nonabsolute type which include the spaces c 0 $c_{0}$ and c, respectively. Also, we prove that the spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ are linearly isomorphic to the spaces c 0 $c_{0}$ and c, in turn, and we investigate some inclusion relations. Moreover, we obtain the Schauder bases of those spaces and determine their α-, β-, and γ-duals. Finally, we characterize some matrix classes related to those spaces. |
| first_indexed | 2024-04-12T10:15:38Z |
| format | Article |
| id | doaj.art-24b7c2aef46548428b1cbe0826a809bf |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-12T10:15:38Z |
| publishDate | 2016-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-24b7c2aef46548428b1cbe0826a809bf2022-12-22T03:37:13ZengSpringerOpenJournal of Inequalities and Applications1029-242X2016-11-012016111610.1186/s13660-016-1256-0The binomial sequence spaces of nonabsolute typeMustafa Cemil Bişgin0Faculty Of Arts And Sciences, Department Of Mathematics, Recep Tayyip Erdoğan UniversityAbstract In this paper, we introduce the binomial sequence spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ of nonabsolute type which include the spaces c 0 $c_{0}$ and c, respectively. Also, we prove that the spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ are linearly isomorphic to the spaces c 0 $c_{0}$ and c, in turn, and we investigate some inclusion relations. Moreover, we obtain the Schauder bases of those spaces and determine their α-, β-, and γ-duals. Finally, we characterize some matrix classes related to those spaces.http://link.springer.com/article/10.1186/s13660-016-1256-0matrix transformationsmatrix domainSchauder basisα-, β- and γ-dualsmatrix classes |
| spellingShingle | Mustafa Cemil Bişgin The binomial sequence spaces of nonabsolute type Journal of Inequalities and Applications matrix transformations matrix domain Schauder basis α-, β- and γ-duals matrix classes |
| title | The binomial sequence spaces of nonabsolute type |
| title_full | The binomial sequence spaces of nonabsolute type |
| title_fullStr | The binomial sequence spaces of nonabsolute type |
| title_full_unstemmed | The binomial sequence spaces of nonabsolute type |
| title_short | The binomial sequence spaces of nonabsolute type |
| title_sort | binomial sequence spaces of nonabsolute type |
| topic | matrix transformations matrix domain Schauder basis α-, β- and γ-duals matrix classes |
| url | http://link.springer.com/article/10.1186/s13660-016-1256-0 |
| work_keys_str_mv | AT mustafacemilbisgin thebinomialsequencespacesofnonabsolutetype AT mustafacemilbisgin binomialsequencespacesofnonabsolutetype |