Paranormed Norlund Nᵗ- difference sequence spaces and their α-, β- and γ-duals
| dc.creator | Singh, Sukhdev | |
| dc.creator | Malik, Toseef Ahmed | |
| dc.date | 2023-07-18 | |
| dc.date.accessioned | 2023-07-21T14:31:35Z | |
| dc.date.available | 2023-07-21T14:31:35Z | |
| dc.identifier | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5289 | |
| dc.identifier | 10.22199/issn.0717-6279-5289 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/232378 | |
| dc.description | Kizmaz [4] defined some difference spaces viz., ℓ∞ (∆), c(∆) and c0(∆) and studied by Et and Colak [1] thoroughly. In this paper, Norlund Nt- difference sequence spaces Nt(c0, p, ∆), Nt(c, p, ∆) and Nt(ℓ∞, p, ∆) contain the sequences whose Nt∆-transforms in c0, c and ℓ∞ are defined and the paranormed linear structures are developed on these spaces. It has been shown that the spaces Nt(c0, p, ∆), Nt(c, p, ∆) & Nt(ℓ∞, p, ∆) are linearly isomorphic and are of non-absolute type. Further, it is verified that Nt(c, p, ∆), Nt(c0, p, ∆)and Nt(l∞, p, ∆) of non-absolute form are isomorphic to Nt(c0, p), Nt(c, p) and Nt(ℓ∞, p), respectively. Topological properties such as the completeness and the isomorphism are also discussed. Some inclusion relations among these spaces are also verified. Finally, the α-, β- and γ- dual of these spaces are determined and constructed the Schauder-basis of Nt(c0, p, ∆) and Nt(c, p, ∆). | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad Católica del Norte. | en-US |
| dc.relation | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5289/4326 | |
| dc.rights | Copyright (c) 2023 Sukhdev Singh, Toseef Ahmed Malik | en-US |
| dc.rights | https://creativecommons.org/licenses/by/4.0 | en-US |
| dc.source | Proyecciones (Antofagasta, On line); Vol. 42 No. 4 (2023); 879-892 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 42 Núm. 4 (2023); 879-892 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 10.22199/issn.0717-6279-2023-04 | |
| dc.subject | paranormed sequence space | en-US |
| dc.subject | Nᵗ-Difference sequence space | en-US |
| dc.subject | Norlund matrix | en-US |
| dc.subject | Schauder basis | en-US |
| dc.subject | α-, β- and γ-duals | en-US |
| dc.subject | 40A05 | en-US |
| dc.subject | 46A45 | en-US |
| dc.title | Paranormed Norlund Nᵗ- difference sequence spaces and their α-, β- and γ-duals | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | text | en-US |
| dc.coverage | 20th Century | en-US |
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Proyecciones: Journal of Mathematics
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