On the New Generalized Hahn Sequence Space hdp
In this article, we define the new generalized Hahn sequence space hdp, where d=dkk=1∞ is monotonically increasing sequence with dk≠0 for all k∈ℕ, and 1<p<∞. Then, we prove some topological properties and calculate the α−, β−, and γ−duals of hdp. Furthermore, we characterize the new matrix cla...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2022/6832559 |
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| author | Orhan Tuğ Eberhard Malkowsky Bipan Hazarika Taja Yaying |
| author_facet | Orhan Tuğ Eberhard Malkowsky Bipan Hazarika Taja Yaying |
| author_sort | Orhan Tuğ |
| collection | DOAJ |
| description | In this article, we define the new generalized Hahn sequence space hdp, where d=dkk=1∞ is monotonically increasing sequence with dk≠0 for all k∈ℕ, and 1<p<∞. Then, we prove some topological properties and calculate the α−, β−, and γ−duals of hdp. Furthermore, we characterize the new matrix classes hd,λ, where λ=bv,bvp,bv∞,bs,cs,, and μ,hd, where μ=bv,bv0,bs,cs0,cs. In the last section, we prove the necessary and sufficient conditions of the matrix transformations from hdp into λ=ℓ∞,c,c0,ℓ1,hd,bv,bs,cs, and from μ=ℓ1,bv0,bs,cs0 into hdp. |
| format | Article |
| id | doaj-art-accc7d1559dc4e49ba589f3d772d9be2 |
| institution | OA Journals |
| issn | 1687-0409 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-accc7d1559dc4e49ba589f3d772d9be22025-08-20T02:20:23ZengWileyAbstract and Applied Analysis1687-04092022-01-01202210.1155/2022/6832559On the New Generalized Hahn Sequence Space hdpOrhan Tuğ0Eberhard Malkowsky1Bipan Hazarika2Taja Yaying3Department of Mathematics EducationDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsIn this article, we define the new generalized Hahn sequence space hdp, where d=dkk=1∞ is monotonically increasing sequence with dk≠0 for all k∈ℕ, and 1<p<∞. Then, we prove some topological properties and calculate the α−, β−, and γ−duals of hdp. Furthermore, we characterize the new matrix classes hd,λ, where λ=bv,bvp,bv∞,bs,cs,, and μ,hd, where μ=bv,bv0,bs,cs0,cs. In the last section, we prove the necessary and sufficient conditions of the matrix transformations from hdp into λ=ℓ∞,c,c0,ℓ1,hd,bv,bs,cs, and from μ=ℓ1,bv0,bs,cs0 into hdp.http://dx.doi.org/10.1155/2022/6832559 |
| spellingShingle | Orhan Tuğ Eberhard Malkowsky Bipan Hazarika Taja Yaying On the New Generalized Hahn Sequence Space hdp Abstract and Applied Analysis |
| title | On the New Generalized Hahn Sequence Space hdp |
| title_full | On the New Generalized Hahn Sequence Space hdp |
| title_fullStr | On the New Generalized Hahn Sequence Space hdp |
| title_full_unstemmed | On the New Generalized Hahn Sequence Space hdp |
| title_short | On the New Generalized Hahn Sequence Space hdp |
| title_sort | on the new generalized hahn sequence space hdp |
| url | http://dx.doi.org/10.1155/2022/6832559 |
| work_keys_str_mv | AT orhantug onthenewgeneralizedhahnsequencespacehdp AT eberhardmalkowsky onthenewgeneralizedhahnsequencespacehdp AT bipanhazarika onthenewgeneralizedhahnsequencespacehdp AT tajayaying onthenewgeneralizedhahnsequencespacehdp |