Some q-fractional order difference sequence spaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909916629827584 |
|---|---|
| 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 |