Approximation properties of complex q q -SzszMirakjan operators in compact disks
This paper deals with approximating properties of the newly defined q q -generalization of the SzszMirakjan operators in the case q>1 q > 1 . Quantitative estimates of the convergence, the Voronovskajas theorem and saturation of convergence for complex q q -SzszMirakjan operators attached to analytic functions in compact disks are given. In particular, it is proved that for functions analytic in {z?C:|z| 2q R > 2 q , the rate of approximation by the q q -SzszMirakjan operators (q>1 q > 1 ) is of order q?n q ? n versus 1/n 1 / n for the classical SzszMirakjan operators.
q q -szaszmirakjan operator q q q q q complex approximation voronovskaja-type result