Approximation properties of complex q-Szász–Mirakjan operators in compact disks

AbstractThis paper deals with approximating properties of the newly defined q-generalization of the Szász–Mirakjan operators in the case q>1. Quantitative estimates of the convergence, the Voronovskaja’s theorem and saturation of convergence for complex q-Szász–Mirakjan operators attached to analytic functions in compact disks are given. In particular, it is proved that for functions analytic in {z∈C:|z|<R}, R>2q, the rate of approximation by the q-Szász–Mirakjan operators (q>1) is of order q−n versus 1/n for the classical Szász–Mirakjan operators