Density by Moduli and Lacunary Statistical Convergence
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 equivalen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2016-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2016/9365037 |
| Summary: | 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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| ISSN: | 1085-3375 1687-0409 |