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Analysis, Topology and Applications 2008 (ATA2008)
May 30 - June 4, 2008
Technical Faculty, Cacak, University of Kragujevac
Vrnjacka Banja, Serbia, Serbia

Organizers
Dragan Djurcic, Ljubisa D.R. Kocinac, Malisa R. Zizovic

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Quantitative Voronovskaya-type theorems
by
Heiner Gonska
University of Duisburg-Essen
Coauthors: M. Heilmann, R. Paltanea, P. Pitul, I. Rasa, G. Tachev

We will discuss extensions and generalizations of the classical Voronovskaya theorem for Bernstein operators. As one particular consequence we obtain several known quantitative Korovkin-type theorems for positive linear operators defined on C[0, 1].

More concrete applications will be given for the "genuine Bernstein-Durrmeyer operators" Un, for a class of operators which bridge the gap between them and the classical Bernstein operators Bn, and for one further class of mappings linking the Un to the Durrmeyer operators Mn.

Time permitting, we also discuss Voronovskaya-type theorems in terms of the Ditzian-Totik modulus, in simultaneous approximation, and such for the Schoenberg spline operator.

Date received: May 10, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawq-21.