Convergence of iterates of genuine and ultraspherical Durrmeyer operators to the limiting semigroup: C2-estimates

Abstract

In the present note a general inequality for the degree of approximation of semigroups by iterates of commuting bounded linear operators on Banach spaces is given. Combining this with a recent quantitative Voronovskaja-type result applications to Durrmeyer operators with ultraspherical weights are derived. Our considerations include the genuine Bernstein-Durrmeyer operators.