Blending Type Approximation by GBS Operators of Generalized Bernstein-Durrmeyer Type

摘要

In this article we study an extension of the bivariate generalized Bernstein-Durrmeyer operators based on a non-negative real parameter. For these operators we get a Voronovskaja type theorem, the order of approximation using Peetre's K-functional and the degree of approximation by means of the Lipschitz class. Further, we introduce the generalized boolean sum operators of generalized Bernstein-Durrmeyer type and we estimate the degree of approximation in terms of the mixed modulus of smoothness.