MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Asymptotic behaviour of differentiated Bernstein polynomials
Heiner Gonska and Ioan Raşa

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\uı, among others.

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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