Asymptotic behaviour of differentiated Bernstein polynomials

Authors

  • Heiner Gonska University of Duisburg-Essen, Department of Mathematics, D-47048 Duisburg, Germany Author
  • Ioan Raşa Technical University, Department of Mathematics, RO-400020 Cluj-Napoca, Romania Author

Keywords:

Voronovskaya theorem, Bernstein operators, simultaneous approximation, $k$-th Kantorovich modification, convex operators

Subjects:

41A10, 41A17, 41A25, 41A28, 41A36

Abstract

In the present note we give a full quantitativeversion of a theorem of Floater dealing with the asymptoticbehaviour of differentiated Bernstein polynomials. While Floater'sresult is a generalization of the classical Voronovskaya theorem,ours generalizes a hardly known quantitative version of thistheorem due to Videnski\uı, among others.

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Published

2009-01-15

Issue

Vol. 61 No. 1 (2009): Vol. 61, Issue 1

Section

Articles

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Copyright (c) 2009 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.