A Kantorovich version of Bernstein-type logarithmic operators
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910018833481728 |
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| author | Angeloni, Laura Costarelli, Danilo Darielli, Chiara |
| author_facet | Angeloni, Laura Costarelli, Danilo Darielli, Chiara |
| contents | In this paper, we introduce a Kantorovich version of the Bernstein-type logarithmic operators. The idea comes from the wide literature concerning exponential polynomials that preserve exponential functions: here, the exponential weights are replaced by logarithmic ones and the corresponding operators preserve the logarithmic functions. The pointwise, the uniform and the $L^p$ convergence are first established. Then, a Voronovskaja-type asymptotic formula is derived: from it, a second-order differential operator naturally arises, allowing the characterization of the corresponding saturation class. Finally, quantitative estimates for the order of approximation are provided in the continuous case, in terms of the modulus of continuity, and, in the $L^p$ case, by means of suitable $K$-functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10599 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Kantorovich version of Bernstein-type logarithmic operators Angeloni, Laura Costarelli, Danilo Darielli, Chiara Functional Analysis In this paper, we introduce a Kantorovich version of the Bernstein-type logarithmic operators. The idea comes from the wide literature concerning exponential polynomials that preserve exponential functions: here, the exponential weights are replaced by logarithmic ones and the corresponding operators preserve the logarithmic functions. The pointwise, the uniform and the $L^p$ convergence are first established. Then, a Voronovskaja-type asymptotic formula is derived: from it, a second-order differential operator naturally arises, allowing the characterization of the corresponding saturation class. Finally, quantitative estimates for the order of approximation are provided in the continuous case, in terms of the modulus of continuity, and, in the $L^p$ case, by means of suitable $K$-functionals. |
| title | A Kantorovich version of Bernstein-type logarithmic operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2602.10599 |