Geometric series of positive linear operators and the inverse Voronovskaya theorem on a compact interval - Abel, Ulrich; Ivan, Mircea; Păltănea, Radu (Journal of approximation theory, 2014)
We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our results to the Bernstein operators and a class of Bernstein–Durrmeyer type operators.