In this paper, we investigate approximation properties of the Stancu type generalization of the $\alpha$-Bernstein operator. We obtain a recurrence relation for moments and the rate of convergence by means of moduli of continuity. Also, we present Voronovskaya and Grüss-Voronovskaya type asymptotic results for these operators. Finally, the study contains numerical considerations regarding the constructed operators based on Maple algorithms.
Stancu operators, $\alpha$-Bernstein operators, moduli of continuity, rate of convergence, Voronovskaya type theorem
ÇETİN, NURSEL and RADU, VOICHITA ADRIANA
"Approximation by generalized Bernstein-Stancu operators,"
Turkish Journal of Mathematics: Vol. 43:
4, Article 18.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss4/18