Blending Type Approximation by Bivariate Bernstein- Kantorovich operators

Abstract: Pop and F ˇ arcas [12] introduced the bivariate operators of the Bernstein-Kant orovich type and the associated GBS(Generalized Boolean sum) operators of the Kantorovich type. The concern of this paper is to obtain the rate of conver gence in terms of the partial and complete modulus of continuity an d the degree of approximation by means of Lipschitz class for the above bivariate operators. We also study the simultaneous approx imation for the first order partial derivative of the operato . In the last section, we estimate the degree of approximation by means of the Lipsc hitz lass for B ̈ ogel continuous functions and the rate of convergence with the help of Peetre’s Kfunctional for the GBS operator o f Bernstein-Kantorovich type.