Bernstein operators of second kind and blending systems

Authors

  • Daniela Ioana Inoan Technical University of Cluj-Napoca, Department of Mathematics, Romania
  • Fadel Nasaireh Technical University of Cluj-Napoca, Department of Mathematics, Romania
  • Ioan Rasa Technical University of Cluj-Napoca, Department of Mathematics, Romania https://orcid.org/0000-0002-5206-030X

DOI:

https://doi.org/10.33993/jnaat461-1103

Keywords:

blending system, total positivity, shape preserving properties
Abstract views: 283

Abstract

We consider the fundamental polynomials associated with the Bernstein operators of second kind. They form a blending system for which we study some shape preserving properties.
Modified operators are introduced; they have better interpolation properties. The corresponding blending system is also studied.

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References

J.M. Carnicer, M. Garcıa-Esnaola, J.M. Pena, Bases with Convexity Preserving Properties, Advanced Topics in Multivariate Approximation, F.Fontanella, K. Jetter and P.J. Laurent (eds.), World Scientific Publishing 1996, pp. 17-31.

J.M. Carnicer, M. Garcıa-Esnaola, J.M. Pena, Convexity of rational curves and total positivity, J. Comput. Appl. Math., 71 (2) (1996), pp. 365-382, https://doi.org/10.1016/0377-0427(95)00240-5 DOI: https://doi.org/10.1016/0377-0427(95)00240-5

M.S. Floater, Total Positivity and Convexity Preservation, J. Approx. Theory, 96 (1) (1999), pp. 46-66, http://doi.org/10.1006/jath.1998.3219 DOI: https://doi.org/10.1006/jath.1998.3219

Tim N.T. Goodman, Total Positivity and the Shape of Curves, Total Positivity and its Applications, M. Gasca and Ch. Micchelli (eds.), Kluver Academic Publishers, 1996, pp. 157-186. DOI: https://doi.org/10.1007/978-94-015-8674-0_9

D. Inoan, I. Rasa, A recursive algorithm for Bernstein operators of second kind, Numer.Algor., 64 (4) (2013), pp .699-706, http://doi.org/10.1007/s11075-012-9688-1 DOI: https://doi.org/10.1007/s11075-012-9688-1

S. Karlin, Total Positivity, Stanford University Press, California, 1968.

I. Rasa, Classes of convex functions associated with Bernstein operators of second kind, Math. Ineq. Appl., 9 (4) (2006), pp. 599-605. DOI: https://doi.org/10.7153/mia-09-54

I. Rasa, On Soardi’s Bernstein operators of second kind, Rev. Anal. Numer. Theor. Approx., 29 (2000), no. 2 , pp. 191-199, http://ictp.acad.ro/jnaat/journal/article/view/2000-vol29- no2-art9

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

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Published

2017-09-21

How to Cite

Inoan, D. I., Nasaireh, F., & Rasa, I. (2017). Bernstein operators of second kind and blending systems. J. Numer. Anal. Approx. Theory, 46(1), 47–53. https://doi.org/10.33993/jnaat461-1103

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