Approximation by the q -Szász-Mirakjan Operators

Abstract

This paper deals with approximating properties of the q-generalization of the Szász-Mirakjan 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-Mirakjan operators ($q>1$ ) is of order $q^{-n}$ versus 1/n for the classical Szász-Mirakjan operators.