Skip to main content
SpringerLink
Log in

The moments for q-Bernstein operators in the case 0 < q < 1

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

In this note we give the estimates of the central moments for q-Bernstein operators (0 < q < 1) which can be used for studying the approximation properties of the operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ditzian, Z., Totik, V.: Moduli of Smoothness. Springer, New York (1987)

    MATH  Google Scholar 

  2. Derriennic, M.-M.: Modifed Bernstein polynomials and Jacobi polynomials in q-calculus. Rend. Circ. Mat. Palermo (II)(Suppl. 76), 269–290 (2005)

    Google Scholar 

  3. II’nskii, A., Ostrovska, S.: Convergence of generalized Bernstein polynomials. J. Approx. Theory 116, 100–112 (2002)

    Article  MathSciNet  Google Scholar 

  4. Lewanowicz, S., Wozny, P.: Generalized Bernstein polynomials. BIT 44, 63–78 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Lupaş, A.: A q-analogue of the Bernstein operator. In: Seminar on Numerical and Statistical Calculus, vol. 9, University of Cluj-Napoca (1987)

  6. Mahmudov, N.I.: Korovkin-type theorems and applications. Cent. Eur. J. Math. doi:10.2478/s11533-009-0006-7

  7. Ostrovska, S.: The first decade of the q-Bernstein polynomials: results and perspectives. J. Math. Anal. Approx. Theory 2, 35–51 (2007)

    MATH  MathSciNet  Google Scholar 

  8. Ostrovska, S.: On the Lupaş q-analogue of the Bernstein operator. Rocky Mt. J. Math. 36, 1615–1629 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ostrovska, S.: The convergence of q-Bernstein polynomials (0 < q < 1) in the complex plane. Math. Nachr. 282(2), 243–252 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Phillips, G.M.: Interpolation and Approximation by Polynomials. Springer, New York (2003)

    MATH  Google Scholar 

  11. Videnskii, V.S.: On some classes of q-parametric positive linear operators. In: Selected Topics in Complex Analysis. Oper. Theory Adv. Appl., vol. 158, pp. 213–222. Birkhäuser, Basel (2005)

    Chapter  Google Scholar 

  12. Wang, H.: Korovkin-type theorem and application J. Approx. Theory 132, 258–264 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Wang, H.: Properties of convergence for ω, q-Bernstein polynomials. J. Math. Anal. Appl. 340, 1096–1108 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Wang, H.: Shape-preserving properties of ω,q-Bernstein polynomials. Linear Algebra Appl. 430, 957–967 (2009)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin, 10, Turkey

    Nazim Mahmudov

Authors
  1. Nazim Mahmudov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nazim Mahmudov.

Additional information

The research is supported by the Ministry of National Education and Culture of TRNC under Project MEKB-07-05 and by the Research Advisory Board of Eastern Mediterranean University under Project BAP-A-08-04.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mahmudov, N. The moments for q-Bernstein operators in the case 0 < q < 1. Numer Algor 53, 439–450 (2010). https://doi.org/10.1007/s11075-009-9312-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-009-9312-1

Keywords

Search

Navigation