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...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2016/9365037 |
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| author | Vinod K. Bhardwaj Shweta Dhawan |
| author_facet | Vinod K. Bhardwaj Shweta Dhawan |
| author_sort | Vinod K. Bhardwaj |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d0971e6216124cbf912ac5381fa4d78e |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d0971e6216124cbf912ac5381fa4d78e2025-08-20T03:19:37ZengWileyAbstract and Applied Analysis1085-33751687-04092016-01-01201610.1155/2016/93650379365037Density by Moduli and Lacunary Statistical ConvergenceVinod K. Bhardwaj0Shweta Dhawan1Department of Mathematics, Kurukshetra University, Kurukshetra 136119, IndiaDepartment of Mathematics, KVA DAV College for Women, Karnal 132001, IndiaWe 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.http://dx.doi.org/10.1155/2016/9365037 |
| spellingShingle | Vinod K. Bhardwaj Shweta Dhawan Density by Moduli and Lacunary Statistical Convergence Abstract and Applied Analysis |
| title | Density by Moduli and Lacunary Statistical Convergence |
| title_full | Density by Moduli and Lacunary Statistical Convergence |
| title_fullStr | Density by Moduli and Lacunary Statistical Convergence |
| title_full_unstemmed | Density by Moduli and Lacunary Statistical Convergence |
| title_short | Density by Moduli and Lacunary Statistical Convergence |
| title_sort | density by moduli and lacunary statistical convergence |
| url | http://dx.doi.org/10.1155/2016/9365037 |
| work_keys_str_mv | AT vinodkbhardwaj densitybymoduliandlacunarystatisticalconvergence AT shwetadhawan densitybymoduliandlacunarystatisticalconvergence |