Some Topological and Geometrical Properties of a New Difference Sequence Space
We introduce the new difference sequence space 𝑎𝑟𝑝(Δ) . Further, it is proved that the space 𝑎𝑟𝑝(Δ) is the BK-space including the space 𝑏𝑣𝑝, which is the space of sequences of pbounded variation. We also show that the spaces 𝑎𝑟𝑝(Δ), and ℓ𝑝 are linearly isomorphic for 1≤𝑝<∞. Furthermore, the b...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/213878 |
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| author | Serkan Demiriz Celal Çakan |
| author_facet | Serkan Demiriz Celal Çakan |
| author_sort | Serkan Demiriz |
| collection | DOAJ |
| description | We introduce the new difference sequence space 𝑎𝑟𝑝(Δ) . Further, it is
proved that the space 𝑎𝑟𝑝(Δ) is the BK-space including the space 𝑏𝑣𝑝, which is the space of sequences of pbounded
variation. We also show that the spaces 𝑎𝑟𝑝(Δ), and ℓ𝑝 are linearly isomorphic for 1≤𝑝<∞.
Furthermore, the basis and the 𝛼-, 𝛽- and
𝛾-duals of the space 𝑎𝑟𝑝(Δ) are determined. We devote
the final section of the paper to examine some geometric properties of the space 𝑎𝑟𝑝(Δ). |
| format | Article |
| id | doaj-art-367650bf199f4d7d837b48e49963bf5c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-367650bf199f4d7d837b48e49963bf5c2025-08-20T03:55:07ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/213878213878Some Topological and Geometrical Properties of a New Difference Sequence SpaceSerkan Demiriz0Celal Çakan1Department of Mathematics, Faculty of Arts and Science, Gaziosmanpaşa University, 60250 Tokat, TurkeyFaculty of Education, Inönü University, 44280 Malatya, TurkeyWe introduce the new difference sequence space 𝑎𝑟𝑝(Δ) . Further, it is proved that the space 𝑎𝑟𝑝(Δ) is the BK-space including the space 𝑏𝑣𝑝, which is the space of sequences of pbounded variation. We also show that the spaces 𝑎𝑟𝑝(Δ), and ℓ𝑝 are linearly isomorphic for 1≤𝑝<∞. Furthermore, the basis and the 𝛼-, 𝛽- and 𝛾-duals of the space 𝑎𝑟𝑝(Δ) are determined. We devote the final section of the paper to examine some geometric properties of the space 𝑎𝑟𝑝(Δ).http://dx.doi.org/10.1155/2011/213878 |
| spellingShingle | Serkan Demiriz Celal Çakan Some Topological and Geometrical Properties of a New Difference Sequence Space Abstract and Applied Analysis |
| title | Some Topological and Geometrical Properties of a New Difference Sequence Space |
| title_full | Some Topological and Geometrical Properties of a New Difference Sequence Space |
| title_fullStr | Some Topological and Geometrical Properties of a New Difference Sequence Space |
| title_full_unstemmed | Some Topological and Geometrical Properties of a New Difference Sequence Space |
| title_short | Some Topological and Geometrical Properties of a New Difference Sequence Space |
| title_sort | some topological and geometrical properties of a new difference sequence space |
| url | http://dx.doi.org/10.1155/2011/213878 |
| work_keys_str_mv | AT serkandemiriz sometopologicalandgeometricalpropertiesofanewdifferencesequencespace AT celalcakan sometopologicalandgeometricalpropertiesofanewdifferencesequencespace |