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In this article, we establish an extension of the bivariate generalization of the  q -Bernstein type operators involving parameter  λ and extension of GBS (Generalized Boolean Sum) operators of bivariate  q -Bernstein type. For the first operators, we state the Volkov-type theorem and we obtain a Voronovskaja type and investigate the degree of approximation by means of the Lipschitz type space. For the GBS type operators, we establish their degree of approximation in terms of the mixed modulus of smoothness. The comparison of convergence of the bivariate  q -Bernstein type operators based on parameters and its GBS type operators is shown by illustrative graphics using MATLAB software.

journal of function spaces

On the Approximation Properties of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>q</mi> <mo>−</mo> </math>Analogue Bivariate <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>λ</mi> </math>-Bernstein Type Operators

On the Approximation Properties of q − Analogue Bivariate λ -Bernstein Type Operators

On the Approximation Properties of $q -$ Analogue Bivariate $λ$ -Bernstein Type Operators