An intermediate Voronovskaja type theorem (Q2317580)

For suitable sequences of positive linear operators \(V_n : C[a,b]\rightarrow C[a,b]\) the classical Voronovskaja type results evaluate the limit \(\lim_{n\rightarrow \infty}n(V_n f(x)-f(x))\) where \(f \in C[a,b]\) is twice differentiable at \(x\). The author obtains a Voronovskaja type result of the form \(\lim_{n\rightarrow \infty}\lambda_n(V_n f(x)-f(x))=A_0(x)f(x)+A_1(x)f'(x)\), with \(f\) differentiable at \(x\) and \(\lambda_n\rightarrow \infty\) satisfying suitable hypotheses. Applications of the general results are provided.