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

This 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 Voronovskajaʹs 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 fz 2 C V jzj < Rg, 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.