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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Main Authors: Serkan Demiriz, Celal Çakan
Format: Article
Language:English
Published: Wiley 2011-01-01
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).
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institution Kabale University
issn 1085-3375
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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