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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.

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