Approximation Properties of the q-Balazs-Szabados Complex Operators in the Case q ? 1

Abstract

This paper deals with approximation properties of the newly defined q-generalization of the Balazs-Szabados complex operators in the case . Quantitative estimates of the convergence and Voronovskaja-type theorem are given. In particular, it is shown that the rate of approximation by the q-Balazs-Szabados () is of order versus 1 / n for the classical Balazs-Szabados () operators. The results are new even for the classical case q = 1.