Some q-fractional order difference sequence spaces
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909916629827584 |
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| author | Yaying, Taja Baliarsingh, Pinakadhar Hazarika, Bipan |
| author_facet | Yaying, Taja Baliarsingh, Pinakadhar Hazarika, Bipan |
| contents | This paper intends to develop a $q$-difference operator $\nabla^{(γ)}_q$ of fractional order $γ$, and give several intriguing properties of this new difference operator. Our main focus remains on the construction of sequence spaces $\ell_p(\nabla^{(γ)})$ and $\ell_\infty (\nabla^{(γ)})$, at the same time comparing these spaces with those already exist in the literature. Apart from obtaining Schauder basis, we determine $α$-, $β$-, and $γ$-duals of the newly defined spaces. A section is also devoted for characterizing matrix classes $(\ell_p(\nabla^{(γ)}),\mathfrak X),$ where $\mathfrak X$ is any of the spaces $\ell_\infty,$ $c,$ $c_0$ and $\ell_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some q-fractional order difference sequence spaces Yaying, Taja Baliarsingh, Pinakadhar Hazarika, Bipan Functional Analysis This paper intends to develop a $q$-difference operator $\nabla^{(γ)}_q$ of fractional order $γ$, and give several intriguing properties of this new difference operator. Our main focus remains on the construction of sequence spaces $\ell_p(\nabla^{(γ)})$ and $\ell_\infty (\nabla^{(γ)})$, at the same time comparing these spaces with those already exist in the literature. Apart from obtaining Schauder basis, we determine $α$-, $β$-, and $γ$-duals of the newly defined spaces. A section is also devoted for characterizing matrix classes $(\ell_p(\nabla^{(γ)}),\mathfrak X),$ where $\mathfrak X$ is any of the spaces $\ell_\infty,$ $c,$ $c_0$ and $\ell_1$. |
| title | Some q-fractional order difference sequence spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2511.17538 |