Approximation by generalized Bernstein-Stancu operators

Authors

NURSEL ÇETİN
VOICHITA ADRIANA RADU

DOI

10.3906/mat-1903-109

Abstract

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.

Keywords

Stancu operators, $\alpha$-Bernstein operators, moduli of continuity, rate of convergence, Voronovskaya type theorem

First Page

2032

Last Page

2048

Recommended Citation

ÇETİN, NURSEL and RADU, VOICHITA ADRIANA (2019) "Approximation by generalized Bernstein-Stancu operators," Turkish Journal of Mathematics: Vol. 43: No. 4, Article 18. https://doi.org/10.3906/mat-1903-109
Available at: https://journals.tubitak.gov.tr/math/vol43/iss4/18