  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.
