Degree of Approximation for Bivariate Generalized Bernstein Type Operators

作者：Acar Tuncer^*; Kajla Arun

来源：Results in Mathematics, 2018, 73(2): UNSP 79.

DOI：10.1007/s00025-018-0838-1

• GBS operators
• B-continuous function
• B-differentiable function
• mixed modulus of smoothness

In this paper we study an extension of the bivariate generalized Bernstein operators based on a non-negative real parameters. For these operators we obtain the order of approximation using Peetre's K-functional, a Voronovskaja type theorem and the degree of approximation by means of the Lipschitz class. Further, we consider the Generalized Boolean Sum operators of generalized Bernstein type and we study the degree of approximation in terms of the mixed modulus of continuity. Finally, we show the comparisons by some illustrative graphics in Maple for the convergence of the operators to certain functions.

• 出版日期2018-6