Approximation by generalized Bernstein-Stancu operators

Authors: NURSEL ÇETİN, VOICHITA ADRIANA RADU

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

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