Quantitative q-Voronovskaya and q-Grüss–Voronovskaya-type results for q-Szász operators

In the present paper, we mainly study quantitative Voronovskaya-type theorems for q -Szász operators defined in [20]. We consider weighted spaces of functions and the corresponding weighted modulus of continuity. We obtain the quantitative q -Voronovskaya-type theorem and the q -Grüss–Voronovskaya-type theorem in terms of the weighted modulus of continuity of q -derivatives of the approximated function. In this way, we either obtain the rate of pointwise convergence of q -Szász operators or we present these results for a subspace of continuous functions, although the classical ones are valid for differentiable functions.