Approximation properties of bivariate complex q-Bernstein polynomials in the case q > 1

In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate q-Bernstein polynomials for a function analytic in the polydisc \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D_{{R_1}}} \times {D_{{R_2}}} = \{ z \in C:\left| z \right| < {R_1}\} \times \{ z \in C:\left| z \right| < {R_1}\} $$\end{document} for arbitrary fixed q > 1. We give quantitative Voronovskaja type estimates for the bivariate q-Bernstein polynomials for q > 1. In the univariate case the similar results were obtained by S.Ostrovska: q-Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255, and S.G.Gal: Approximation by Complex Bernstein and Convolution Type Operators. Series on Concrete and Applicable Mathematics 8. World Scientific, New York, 2009.