Density by Moduli and Lacunary Statistical Convergence

Vinod K. Bhardwaj and Shweta Dhawan

Abstract and Applied Analysis, 2016, vol. 2016, issue 1

Abstract: 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.

Date: 2016
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https://doi.org/10.1155/2016/9365037

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:9365037

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