Approximation by q-Szasz operators

Abstract

his paper deals with approximating properties of the newly defined $q$-generalization of the Szász operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by the $q$-Szász operators ($q>1$) is of order $q^{-n}$ versus $1/n$ for the classical Szász--Mirakjan operators.