Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order
We generalize the lacunary statistical convergence by introducing the generalized difference operator Δνα of fractional order, where α is a proper fraction and ν=(νk) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological s...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2015/984283 |
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| author | Ugur Kadak |
| author_facet | Ugur Kadak |
| author_sort | Ugur Kadak |
| collection | DOAJ |
| description | We generalize the lacunary statistical convergence by introducing the generalized difference operator Δνα of fractional order, where α is a proper fraction and ν=(νk) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological structures of related sequence spaces. Furthermore, we introduce some properties of the strongly Cesaro difference sequence spaces of fractional order involving lacunary sequences and examine various inclusion relations of these spaces. We also determine the relationship between lacunary statistical and strong Cesaro difference sequence spaces of fractional order. |
| format | Article |
| id | doaj-art-aff54109b72a4e2e9a2e02e4ba65820d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-aff54109b72a4e2e9a2e02e4ba65820d2025-02-03T05:45:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252015-01-01201510.1155/2015/984283984283Generalized Lacunary Statistical Difference Sequence Spaces of Fractional OrderUgur Kadak0Department of Mathematics, Bozok University, Yozgat, TurkeyWe generalize the lacunary statistical convergence by introducing the generalized difference operator Δνα of fractional order, where α is a proper fraction and ν=(νk) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological structures of related sequence spaces. Furthermore, we introduce some properties of the strongly Cesaro difference sequence spaces of fractional order involving lacunary sequences and examine various inclusion relations of these spaces. We also determine the relationship between lacunary statistical and strong Cesaro difference sequence spaces of fractional order.http://dx.doi.org/10.1155/2015/984283 |
| spellingShingle | Ugur Kadak Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order International Journal of Mathematics and Mathematical Sciences |
| title | Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order |
| title_full | Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order |
| title_fullStr | Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order |
| title_full_unstemmed | Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order |
| title_short | Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order |
| title_sort | generalized lacunary statistical difference sequence spaces of fractional order |
| url | http://dx.doi.org/10.1155/2015/984283 |
| work_keys_str_mv | AT ugurkadak generalizedlacunarystatisticaldifferencesequencespacesoffractionalorder |