A new Representation of $α$-Bernstein Operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911162396835840 |
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| author | Saeidian, Jamshid Nouri, Bahareh |
| author_facet | Saeidian, Jamshid Nouri, Bahareh |
| contents | The $α$-Bernstein operators were initially introduced in the paper by Chen, X., Tan, J., Liu, Z., Xie, J. (2017) titled "Approximation of Functions by a New Family of Generalized Bernstein Operators" (Journal of Mathematical Analysis and Applications, 450(1), 244-261). Since their introduction, these operators have served as a source of inspiration for numerous research endeavors. In this study, we propose a novel technique, founded on a recursive relation, for constructing Bernstein-like bases. A special case of this new representation yields a novel portrayal of Chen's operators. This innovative representation enables the discovery of additional properties of $α$-Bernstein operators and facilitates alternative and more straightforward proofs for certain theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new Representation of $α$-Bernstein Operators Saeidian, Jamshid Nouri, Bahareh Classical Analysis and ODEs Numerical Analysis The $α$-Bernstein operators were initially introduced in the paper by Chen, X., Tan, J., Liu, Z., Xie, J. (2017) titled "Approximation of Functions by a New Family of Generalized Bernstein Operators" (Journal of Mathematical Analysis and Applications, 450(1), 244-261). Since their introduction, these operators have served as a source of inspiration for numerous research endeavors. In this study, we propose a novel technique, founded on a recursive relation, for constructing Bernstein-like bases. A special case of this new representation yields a novel portrayal of Chen's operators. This innovative representation enables the discovery of additional properties of $α$-Bernstein operators and facilitates alternative and more straightforward proofs for certain theorems. |
| title | A new Representation of $α$-Bernstein Operators |
| topic | Classical Analysis and ODEs Numerical Analysis |
| url | https://arxiv.org/abs/2407.16175 |