Approximation properties of bivariate complex q-Bernstein polynomials in the case q>1
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 557-566.

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In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate q-Bernstein polynomials for a function analytic in the polydisc DR1×DR2={zC:|z| 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.
DOI : 10.1007/s10587-012-0029-2
Classification : 33D15, 41A10, 41A35
Mots-clés : q-Bernstein polynomials; modulus of continuity; Voronovskaja type theorem
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Mahmudov, Nazim I. Approximation properties of bivariate complex $q$-Bernstein polynomials in the case $q>1$. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 557-566. doi : 10.1007/s10587-012-0029-2. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0029-2/

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