Approximation by q-Szasz operators

his paper deals with approximating properties of the newly defined $q$-generalization of the Sz\'{a}sz 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 $q$-Sz\'{a}sz operators ($q>1$) is of order $q^{-n}$ versus $1/n$ for the classical Sz\'{a}sz--Mirakjan operators

Voronovskaja type theorem for the Lupaş q-analogue of the Bernstein operators

In this paper, we estimate the third and the fourth order central moments for the difference of the Lupaş q-analogue of the Bernstein operator and the limit q-Lupaş operator. We also prove a quantitative variant of Voronovskaja\u27s theorem for $R_{n,q}$