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2016 Density by Moduli and Lacunary Statistical Convergence
Vinod K. Bhardwaj, Shweta Dhawan
Abstr. Appl. Anal. 2016: 1-11 (2016). DOI: 10.1155/2016/9365037


We have introduced and studied a new concept of f-lacunary statistical convergence, where f is an unbounded modulus. It is shown that, under certain conditions on a modulus f, the concepts of lacunary strong convergence with respect to a modulus f and f-lacunary statistical convergence are equivalent on bounded sequences. We further characterize those θ for which Sθf=Sf, where Sθf and Sf denote the sets of all f-lacunary statistically convergent sequences and f-statistically convergent sequences, respectively. A general description of inclusion between two arbitrary lacunary methods of f-statistical convergence is given. Finally, we give an Sθf-analog of the Cauchy criterion for convergence and a Tauberian theorem for Sθf-convergence is also proved.


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Vinod K. Bhardwaj. Shweta Dhawan. "Density by Moduli and Lacunary Statistical Convergence." Abstr. Appl. Anal. 2016 1 - 11, 2016.


Received: 15 November 2015; Accepted: 5 January 2016; Published: 2016
First available in Project Euclid: 13 April 2016

zbMATH: 1376.40002
MathSciNet: MR3465029
Digital Object Identifier: 10.1155/2016/9365037

Rights: Copyright © 2016 Hindawi

Vol.2016 • 2016
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