On Soardi's Bernstein operators of second kind

Authors

  • Ioan Raşa Technical University of Cluj-Napoca

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.

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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

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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

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

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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. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2000-vol29-no2-art9

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