Sur la suite des opérateurs Bernstein composés

On the sequence of composite Bernstein operators

Authors

  • H. Gonska University of Duisburg-Essen, Germany
  • I. Raşa Technical University of Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat422-990

Keywords:

composite Bernstein operators, composite quadrature formulas, modulus of continuity, degree of approximation, inequalities of Chebyshev-Grüss type
Abstract views: 269

Abstract

We consider a sequence of composite Bernstein operators and the quadrature formulae associated with them. Upper bounds for the approximation error of continuous functions and for the approximation of integrals of continuous functions are given. The bounds are described in terms of moduli of continuity of order one and two. Two inequalities of Tchebycheff-Grüss-type are also included.

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References

D. Barbosu and D. Miclauş, On the composite Bernstein type quadrature formula, Rev. Anal. Numér. Théor. Approx., 39 (2010) no. 1, pp. 3-7, http://ictp.acad.ro/jnaat/journal/article/view/2010-vol39-no1-art1

H. Gonska, D. Kacsó and P. Piţul, The degree of convergence of over-iterated positive linear operators, J. Appl. Funct. Anal., 1 (2006) no. 4, pp. 403-423.

H.H. Gonska and R.K. Kovacheva The second order modulus revisited: remarks, applications, problems, Confer. Sem. Mat. Univ. Bari, 32 (1994) no. 257, pp. (1995).

H. Gonska, I. Raşa and M.-D.Rusu, Čebyšev-Grüss-type inequalities revisited, Math. Slovaca, 63 (2013) no. 5, 1007-1024. DOI: https://doi.org/10.2478/s12175-013-0151-0

R. Paltanea, Approximation Theory using Positive Linear Operators, Birkhäuser Boston, Inc., Boston, MA, 2004. DOI: https://doi.org/10.1007/978-1-4612-2058-9

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Published

2013-08-01

How to Cite

Gonska, H., & Raşa, I. (2013). Sur la suite des opérateurs Bernstein composés: On the sequence of composite Bernstein operators. Rev. Anal. Numér. Théor. Approx., 42(2), 151–160. https://doi.org/10.33993/jnaat422-990

Issue

Vol. 42 No. 2 (2013)

Section

Articles

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

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