Blending type approximation by bivariate generalized Bernstein type operators

Abstract

In this article we establish an extension of the bivariate generalization of the Bernstein type operators involving parameters. For these operators we obtain a Voronovskaja type and Grüss Voronovskaja type theorems and the degree of approximation by means of the Lipschitz type space. Further, we present the associated Generalized Boolean Sum (GBS) operators and establish their degree of approximation in terms of the mixed modulus of smoothness. The comparison of convergence of the bivariate Bernstein type operators based on parameters and its GBS type operators is shown by illustrative graphics using MAPLE software.

Mathematics Subject Classification (2010): 41A25, 26A15.