Approximation by the q-Szasz-Mirakjan Operators

Abstract

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