The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv
Most recently, the generalized difference operator Δi3 of order three was defined and its domain in Hahn sequence space h was calculated. In this paper, the spaces ℓ1Δi3 and bvΔi3 are introduced as the domain of generalized difference operator Δi3 of order three in the sequence spaces ℓ1 and bv. The...
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| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6343084 |
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| author | Orhan Tuğ |
| author_facet | Orhan Tuğ |
| author_sort | Orhan Tuğ |
| collection | DOAJ |
| description | Most recently, the generalized difference operator Δi3 of order three was defined and its domain in Hahn sequence space h was calculated. In this paper, the spaces ℓ1Δi3 and bvΔi3 are introduced as the domain of generalized difference operator Δi3 of order three in the sequence spaces ℓ1 and bv. Then, some topological properties of ℓ1Δi3 and bvΔi3 are given, and some inclusion relations are shown. Additionally, algebraic dual, α−, β−, and γ− dual spaces of ℓ1Δi3 and bvΔi3 are computed. In the last section, the classes μΔi3:λ and λ:μΔi3 of matrix transformations are characterized, where μ=ℓ1,bv and λ=c,c0,ℓ1,ℓ∞,bs,cs,bv,h. |
| format | Article |
| id | doaj-art-3048012ca6544afbb1eb2d7c4afb242e |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3048012ca6544afbb1eb2d7c4afb242e2025-02-03T06:13:30ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/6343084The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bvOrhan Tuğ0Department of Mathematics EducationMost recently, the generalized difference operator Δi3 of order three was defined and its domain in Hahn sequence space h was calculated. In this paper, the spaces ℓ1Δi3 and bvΔi3 are introduced as the domain of generalized difference operator Δi3 of order three in the sequence spaces ℓ1 and bv. Then, some topological properties of ℓ1Δi3 and bvΔi3 are given, and some inclusion relations are shown. Additionally, algebraic dual, α−, β−, and γ− dual spaces of ℓ1Δi3 and bvΔi3 are computed. In the last section, the classes μΔi3:λ and λ:μΔi3 of matrix transformations are characterized, where μ=ℓ1,bv and λ=c,c0,ℓ1,ℓ∞,bs,cs,bv,h.http://dx.doi.org/10.1155/2022/6343084 |
| spellingShingle | Orhan Tuğ The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv Journal of Mathematics |
| title | The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv |
| title_full | The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv |
| title_fullStr | The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv |
| title_full_unstemmed | The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv |
| title_short | The Generalized Difference Operator Δi3 of Order Three and Its Domain in the Sequence Spaces ℓ1 and bv |
| title_sort | generalized difference operator δi3 of order three and its domain in the sequence spaces l1 and bv |
| url | http://dx.doi.org/10.1155/2022/6343084 |
| work_keys_str_mv | AT orhantug thegeneralizeddifferenceoperatordi3oforderthreeanditsdomaininthesequencespacesl1andbv AT orhantug generalizeddifferenceoperatordi3oforderthreeanditsdomaininthesequencespacesl1andbv |