A Durrmeyer-type variant of Grünwald Interpolation Operators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917425398677504 |
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| author | Vinaya, P. C. |
| author_facet | Vinaya, P. C. |
| contents | In this paper, we construct a Durrmeyer-type variant of Grünwald interpolation operators on the space $L^p[0,π]$. We prove their fundamental properties, including boundedness and convergence in the $L^p$-norm. We establish the convergence results using a Korovkin-type theorem in the setting of Banach function spaces. Furthermore, we obtain quantitative estimates for the convergence by means of the modulus of continuity and an appropriate $K$-functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19190 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Durrmeyer-type variant of Grünwald Interpolation Operators Vinaya, P. C. Functional Analysis 41A05, 41A10, 41A25, 41A35 In this paper, we construct a Durrmeyer-type variant of Grünwald interpolation operators on the space $L^p[0,π]$. We prove their fundamental properties, including boundedness and convergence in the $L^p$-norm. We establish the convergence results using a Korovkin-type theorem in the setting of Banach function spaces. Furthermore, we obtain quantitative estimates for the convergence by means of the modulus of continuity and an appropriate $K$-functional. |
| title | A Durrmeyer-type variant of Grünwald Interpolation Operators |
| topic | Functional Analysis 41A05, 41A10, 41A25, 41A35 |
| url | https://arxiv.org/abs/2604.19190 |