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Pop and Fˇ arcas [12] introduced the bivariate operators of the Bernstein-Kantorovich type and the associated GBS(Generalized Boolean sum) operators of the Kantorovich type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz class for the above bivariate operators. We also study the simultaneous approximation for the first order partial derivative of the operator. In the last section, we estimate the degree of approximation by means of the Lipschitz class for B¨ ogel continuous functions and the rate of convergence with the help of Peetre’s K- functional for the GBS operator of Bernstein-Kantorovich type

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