Modified α-Bernstein operators with better approximation properties

Abstract

In the present note, following a new approach recently described by Khosravian-Arab, Dehghan, and Eslahchi, we construct a new kind of $\alpha$-Bernstein operator and study a uniform convergence estimate for these operators. We also prove some direct results involving the asymptotic theorems. Finally, we illustrate the convergence of the operators to a certain function with the help of Maple software.