On Soardi's Bernstein operators of second kind

Authors

  • Ioan Raşa Technical University of Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat292-669
Abstract views: 231

Abstract

We solve a problem, raised by Paolo Soardi, concerning the shape preserving properties of the Bernstein operators of second kind. We establish also a Voronovskaja-type formula for these operators.

Downloads

Download data is not yet available.

References

F. Altomare, M. Campiti, Korovkin-type approximation theory and its applications, Walter de Gruyter, Berlin-New York, 1994, https://doi.org/10.1515/9783110884586 DOI: https://doi.org/10.1515/9783110884586

G. A. Anastassiou, C. Cottin, H. H. Gonska, Global smoothness of approximating functions, Analysis 11(1991), 43-57. DOI: https://doi.org/10.1524/anly.1991.11.1.43

T.N.T. Goodman, Total positivity and the shape of curves, in: Total positivity and its applications, M. Gasca and C. A. Micchelli (Eds.), Kluwer Academic Publishers, Dordrecht, 1996, pp.157-186, https://doi.org/10.1007/978-94-015-8674-0_9 DOI: https://doi.org/10.1007/978-94-015-8674-0_9

S. Karlin, Total positivity, Stanford University Press, Standford, 1968.

G. G. Lorentz, Bernstein polynomials, Chelsea, New York, 1986.

P. Soardi, Bernstein polynomials and random walks on hypergroups, in: Probability measures on groups, X (Oberwolfach 1990), Plenum, New York, 1991, pp.387-393, https://doi.org/10.1007/978-1-4899-2364-6_29 DOI: https://doi.org/10.1007/978-1-4899-2364-6_29

Downloads

Published

2000-08-01

How to Cite

Raşa, I. (2000). On Soardi’s Bernstein operators of second kind. Rev. Anal. Numér. Théor. Approx., 29(2), 191–199. https://doi.org/10.33993/jnaat292-669

Issue

Vol. 29 No. 2 (2000)

Section

Articles

License

Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

Creative Commons License

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

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.