Abstract
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.
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