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

This paper deals with approximating properties of the newly defined qq-generalization of the Szász–Mirakjan operators in the case q>1q>1. Quantitative estimates of the convergence, the Voronovskaja’s theorem and saturation of convergence for complex qq-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|2qR>2q, the rate of approximation by the qq-Szász–Mirakjan operators (q>1q>1) is of order q−nq−n versus 1/n1/n for the classical Szász–Mirakjan operators.