Proposes a novel technique to construct Bernstein-like bases and reveals new properties of alpha-Bernstein operators, suggesting simpler proofs of theorems.
The ?-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 ?-Bernstein operators and facilitates alternative and more straightforward proofs of certain theorems.
No takes yet. Share an insight, caveat, or question.
Saeidian et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: