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Density by Moduli and Lacunary Statistical Convergence
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Journal Article
Density by Moduli and Lacunary Statistical Convergence
2016
Overview
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.
Publisher
Hindawi Limiteds,Hindawi Publishing Corporation,John Wiley & Sons, Inc,Wiley
Subject
