Citation
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
Abstract
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.
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Additional Metadata
Item Type: | Article |
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Divisions: | Faculty of Science Institute for Mathematical Research |
DOI Number: | https://doi.org/10.1186/1029-242X-2014-311 |
Publisher: | Springer Open |
Keywords: | Lacunary sequence; Statistical boundedness; Statistical convergence; Köthe-Toeplitz duals |
Depositing User: | Nurul Ainie Mokhtar |
Date Deposited: | 21 Dec 2015 12:40 |
Last Modified: | 21 Dec 2015 12:40 |
Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1186/1029-242X-2014-311 |
URI: | http://psasir.upm.edu.my/id/eprint/34729 |
Statistic Details: | View Download Statistic |
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