ESTIMATES OF BIVARIATE NEW KANTOROVICH TYPE OF THE BALAZS-SZABADOS OPERATORS BASED ON Q-INTEGERS

. In this paper, we introduce a new generalization of Kantorovich type Bal & aring;zs-Szabados operators for functions in two dimensions. We deduce the explicit formula of the moments and main formulas of central moments with their estimations. We provide a Korovkin-type approximation theorem defined on compact rectangular areas and present the rate of convergence of bivariate Kantorovich-type Bal & aring;zs-Szabados operators using the modulus of continuity on the compact rectangular region. In addition, we present the order of convergence of these new operators in terms of Lipschitz functions, we present the order of approximation with the help of Peetre's K-functional for these new operators, and we also discuss the rate convergence of the Voronovskaya-type theorem. Finally, we provide a numerical example to illustrate the better case of approximate operators.