A new Representation of $\alpha$-Bernstein Operators
<|reference_start|>A new Representation of $\alpha$-Bernstein Operators: The $\alpha$-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 $\alpha$-Bernstein operators and facilitates alternative and more straightforward proofs for certain theorems.<|reference_end|>
@article{saeidian2024a,
    title={A new Representation of $\alpha$-Bernstein Operators},
    author={Jamshid Saeidian and Bahareh Nouri},
    journal={arXiv preprint arXiv:2407.16175},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.16175},
    primaryClass={math.CA cs.NA math.NA}
}