Density by moduli and Wijsman lacunary statistical convergence of sequences of sets
Abstract The main object of this paper is to introduce and study a new concept of f-Wijsman lacunary statistical convergence of sequences of sets, where f is an unbounded modulus. The definition of Wijsman lacunary strong convergence of sequences of sets is extended to a definition of Wijsman lacuna...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2017-01-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1294-2 |
| _version_ | 1819176698836418560 |
|---|---|
| author | Vinod K Bhardwaj Shweta Dhawan |
| author_facet | Vinod K Bhardwaj Shweta Dhawan |
| author_sort | Vinod K Bhardwaj |
| collection | DOAJ |
| description | Abstract The main object of this paper is to introduce and study a new concept of f-Wijsman lacunary statistical convergence of sequences of sets, where f is an unbounded modulus. The definition of Wijsman lacunary strong convergence of sequences of sets is extended to a definition of Wijsman lacunary strong convergence with respect to a modulus for sequences of sets and it is shown that, under certain conditions on a modulus f, the concepts of Wijsman lacunary strong convergence with respect to a modulus f and f-Wijsman lacunary statistical convergence are equivalent on bounded sequences. We further characterize those θ for which WS θ f = WS f $\mathit{WS}_{\theta}^{f} = \mathit{WS}^{f}$ , where WS θ f $\mathit{WS}_{\theta}^{f}$ and WS f $\mathit{WS}^{f}$ denote the sets of all f-Wijsman lacunary statistically convergent sequences and f-Wijsman statistically convergent sequences, respectively. |
| first_indexed | 2024-12-22T21:14:54Z |
| format | Article |
| id | doaj.art-e6a90fa337264601ac9bf5dc3ccb64ca |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-22T21:14:54Z |
| publishDate | 2017-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-e6a90fa337264601ac9bf5dc3ccb64ca2022-12-21T18:12:25ZengSpringerOpenJournal of Inequalities and Applications1029-242X2017-01-012017112010.1186/s13660-017-1294-2Density by moduli and Wijsman lacunary statistical convergence of sequences of setsVinod K Bhardwaj0Shweta Dhawan1Department of Mathematics, Kurukshetra UniversityDepartment of Mathematics, KVA DAV College for WomenAbstract The main object of this paper is to introduce and study a new concept of f-Wijsman lacunary statistical convergence of sequences of sets, where f is an unbounded modulus. The definition of Wijsman lacunary strong convergence of sequences of sets is extended to a definition of Wijsman lacunary strong convergence with respect to a modulus for sequences of sets and it is shown that, under certain conditions on a modulus f, the concepts of Wijsman lacunary strong convergence with respect to a modulus f and f-Wijsman lacunary statistical convergence are equivalent on bounded sequences. We further characterize those θ for which WS θ f = WS f $\mathit{WS}_{\theta}^{f} = \mathit{WS}^{f}$ , where WS θ f $\mathit{WS}_{\theta}^{f}$ and WS f $\mathit{WS}^{f}$ denote the sets of all f-Wijsman lacunary statistically convergent sequences and f-Wijsman statistically convergent sequences, respectively.http://link.springer.com/article/10.1186/s13660-017-1294-2modulus functiondensitylacunary sequencestatistical convergencelacunary strong convergenceWijsman convergence |
| spellingShingle | Vinod K Bhardwaj Shweta Dhawan Density by moduli and Wijsman lacunary statistical convergence of sequences of sets Journal of Inequalities and Applications modulus function density lacunary sequence statistical convergence lacunary strong convergence Wijsman convergence |
| title | Density by moduli and Wijsman lacunary statistical convergence of sequences of sets |
| title_full | Density by moduli and Wijsman lacunary statistical convergence of sequences of sets |
| title_fullStr | Density by moduli and Wijsman lacunary statistical convergence of sequences of sets |
| title_full_unstemmed | Density by moduli and Wijsman lacunary statistical convergence of sequences of sets |
| title_short | Density by moduli and Wijsman lacunary statistical convergence of sequences of sets |
| title_sort | density by moduli and wijsman lacunary statistical convergence of sequences of sets |
| topic | modulus function density lacunary sequence statistical convergence lacunary strong convergence Wijsman convergence |
| url | http://link.springer.com/article/10.1186/s13660-017-1294-2 |
| work_keys_str_mv | AT vinodkbhardwaj densitybymoduliandwijsmanlacunarystatisticalconvergenceofsequencesofsets AT shwetadhawan densitybymoduliandwijsmanlacunarystatisticalconvergenceofsequencesofsets |