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On lacunary statistical boundedness


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
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
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