On lacunary statistical boundedness
A new concept of lacunary statistical boundedness is introduced. It is shown that, for a given lacunary sequence θ={kr}, a sequence {xk} is lacunary statistical bounded if and only if for ‘almost all k w.r.t. θ’, the values xk coincide with those of a bounded sequence. Apart from studying various al...
| Main Authors: | , , , |
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| Format: | Article |
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Springer Open
2014
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| _version_ | 1796972563734200320 |
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| author | Bhardwaj, Vinod K. Gupta, Sandeep Syed Ahmed Mohiuddin, Kilicman, Adem |
| author_facet | Bhardwaj, Vinod K. Gupta, Sandeep Syed Ahmed Mohiuddin, Kilicman, Adem |
| author_sort | Bhardwaj, Vinod K. |
| collection | UPM |
| description | A new concept of lacunary statistical boundedness is introduced. It is shown that, for a given lacunary sequence θ={kr}, a sequence {xk} is lacunary statistical bounded if and only if for ‘almost all k w.r.t. θ’, the values xk coincide with those of a bounded sequence. Apart from studying various algebraic properties and computing the Köthe-Toeplitz duals of the space Sθ(b) of all lacunary statistical bounded sequences, a decomposition theorem is also established. We characterize those θ for which Sθ(b)=S(b). Finally, we give a general description of inclusion between two arbitrary lacunary methods of statistical boundedness. |
| first_indexed | 2024-03-06T08:29:52Z |
| format | Article |
| id | upm.eprints-34729 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-03-06T08:29:52Z |
| publishDate | 2014 |
| publisher | Springer Open |
| record_format | dspace |
| spelling | upm.eprints-347292015-12-21T12:40:23Z http://psasir.upm.edu.my/id/eprint/34729/ On lacunary statistical boundedness Bhardwaj, Vinod K. Gupta, Sandeep Syed Ahmed Mohiuddin, Kilicman, Adem A new concept of lacunary statistical boundedness is introduced. It is shown that, for a given lacunary sequence θ={kr}, a sequence {xk} is lacunary statistical bounded if and only if for ‘almost all k w.r.t. θ’, the values xk coincide with those of a bounded sequence. Apart from studying various algebraic properties and computing the Köthe-Toeplitz duals of the space Sθ(b) of all lacunary statistical bounded sequences, a decomposition theorem is also established. We characterize those θ for which Sθ(b)=S(b). Finally, we give a general description of inclusion between two arbitrary lacunary methods of statistical boundedness. Springer Open 2014 Article PeerReviewed Bhardwaj, Vinod K. and Gupta, Sandeep and Syed Ahmed Mohiuddin, and Kilicman, Adem (2014) On lacunary statistical boundedness. Journal of Inequalities and Applications, 2014. art. no. 311. pp. 1-11. ISSN 1025-5834; ESSN:1029-242X http://www.journalofinequalitiesandapplications.com/content/2014/1/311/abstract 10.1186/1029-242X-2014-311 |
| spellingShingle | Bhardwaj, Vinod K. Gupta, Sandeep Syed Ahmed Mohiuddin, Kilicman, Adem On lacunary statistical boundedness |
| title | On lacunary statistical boundedness |
| title_full | On lacunary statistical boundedness |
| title_fullStr | On lacunary statistical boundedness |
| title_full_unstemmed | On lacunary statistical boundedness |
| title_short | On lacunary statistical boundedness |
| title_sort | on lacunary statistical boundedness |
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