On Hermite type sampling Kantorovich operators in the settings of mixed norm Spaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916775008927744 |
|---|---|
| author | Sonawane, Puja Kumar, A. Sathish |
| author_facet | Sonawane, Puja Kumar, A. Sathish |
| contents | In this paper, we analyze the convergence behavior of Hermite-type sampling Kantorovich operators in the context of mixed norm spaces. We prove certain direct approximation theorems, including the uniform convergence theorem, the Voronovskaja-type asymptotic formula, and an estimate of error in the approximation in terms of the modulus of continuity in mixed norm settings. Next, we estimate the rate of convergence of these sampling Kantorovich operators in terms of the modulus of continuity. In addition, we obtain simultaneous approximation results of these sampling Kantorovich operators, including the uniform approximation, the asymptotic formula, and the approximation error in terms of the modulus of continuity in mixed settings. Finally, using cardinal $B$-splines, the implementation of differentiable functions has been shown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Hermite type sampling Kantorovich operators in the settings of mixed norm Spaces Sonawane, Puja Kumar, A. Sathish Functional Analysis In this paper, we analyze the convergence behavior of Hermite-type sampling Kantorovich operators in the context of mixed norm spaces. We prove certain direct approximation theorems, including the uniform convergence theorem, the Voronovskaja-type asymptotic formula, and an estimate of error in the approximation in terms of the modulus of continuity in mixed norm settings. Next, we estimate the rate of convergence of these sampling Kantorovich operators in terms of the modulus of continuity. In addition, we obtain simultaneous approximation results of these sampling Kantorovich operators, including the uniform approximation, the asymptotic formula, and the approximation error in terms of the modulus of continuity in mixed settings. Finally, using cardinal $B$-splines, the implementation of differentiable functions has been shown. |
| title | On Hermite type sampling Kantorovich operators in the settings of mixed norm Spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2506.02468 |