Abstract

In the present note we give a full quantitative version of a theorem of Floater dealing with the asymptotic behaviour of differentiated Bernstein polynomials. While Floater's result is a generalization of the classical Voronovskaya theorem, ours generalizes a hardly known quantitative version of this theorem due to Videnski\u{\i}, among others.

Keywords: Voronovskaya theorem; Bernstein operators; simultaneous approximation; $k$-th Kantorovich modification; convex operators.

MSC: 41A10, 41A17, 41A25, 41A28, 41A36

Pages:  53$-$61     

Volume  61 ,  Issue  1 ,  2009