Fractional $α$-Bernstein-Kantorovich operators of order $β$: A new construction and approximation results
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910620856614912 |
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| author | Kaur, Jaspreet Goyal, Meenu Ansari, Khursheed J. |
| author_facet | Kaur, Jaspreet Goyal, Meenu Ansari, Khursheed J. |
| contents | In the current article, we establish a distinct version of the operators defined by Berwal \emph{et al.}, which is the Kantorovich type modification of $α$-Bernstein operators to approximate Lebesgue's integrable functions. We define its modification that can preserve the linear function and analyze its characteristics. Additionally, we construct the bivariate of blending type operators by Berwal \emph{et al.}. We analyze both its the convergence and error of approximation properties by using the conventional tools of approximation theory. Finally, we demonstrate our results by presenting examples that highlight graphical visuals using MATLAB. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17594 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional $α$-Bernstein-Kantorovich operators of order $β$: A new construction and approximation results Kaur, Jaspreet Goyal, Meenu Ansari, Khursheed J. Classical Analysis and ODEs In the current article, we establish a distinct version of the operators defined by Berwal \emph{et al.}, which is the Kantorovich type modification of $α$-Bernstein operators to approximate Lebesgue's integrable functions. We define its modification that can preserve the linear function and analyze its characteristics. Additionally, we construct the bivariate of blending type operators by Berwal \emph{et al.}. We analyze both its the convergence and error of approximation properties by using the conventional tools of approximation theory. Finally, we demonstrate our results by presenting examples that highlight graphical visuals using MATLAB. |
| title | Fractional $α$-Bernstein-Kantorovich operators of order $β$: A new construction and approximation results |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2409.17594 |