Skip to main content
SpringerLink
Log in

Approximation of absolutely continuous functions by stancu beta operators

  • Published:
Ukrainian Mathematical Journal Aims and scope

We obtain an exact estimate for the first-order absolute moment of Stancu Beta operators by means of the Stirling formula and integral operations. Then we use this estimate for establishing a theorem on approximation of absolutely continuous functions by Stancu Beta 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. D. D. Stancu, “On the Beta approximation operators of second kind,” Rev. Anal. Numér. Théor. Approx., 2, 231–239 (1995).

    MathSciNet  Google Scholar 

  2. U. Abel, “Asymptotic approximation with Stancu Beta operators,” Rev. Anal. Numér. Théor. Approx., 27, 5–13 (1998).

    MathSciNet  MATH  Google Scholar 

  3. U. Abel and V. Gupta, “Rate of convergence of Stancu Beta operators for functions of bounded variation,” Rev. Anal. Numér. Théor. Approx., 33, 3–9 (2004).

    MathSciNet  MATH  Google Scholar 

  4. V. Gupta, U. Abel, and M. Ivan, “Rate of convergence of Beta operators of second kind for functions with derivatives of bounded variation,” Int. J. Math. Math. Sci., 23, 3827–3833 (2005).

    Article  MathSciNet  Google Scholar 

  5. R. Bojanic and F. Cheng, “Rate of convergence of Bernstein polynomials for functions with derivatives of bounded variation,” J. Math. Anal. Appl., 141, 136–151 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  6. F. Cheng, “On the rate of convergence of Bernstein polynomials of functions of bounded variation,” J. Approx. Theory, 39, 259–274 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Pych-Taberska, “Some properties of the Bézier–Kantorovich type operators,” J. Approx. Theory, 123, 256–269 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  8. X. M. Zeng, “Approximation properties of Gamma operators,” J. Math. Anal. Appl., 311, 389–401 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  9. N. D. Mermin, “Stirling’s formula,” Amer. J. Phys., 52, 362–365 (1984).

    Article  MathSciNet  Google Scholar 

  10. V. Namias, “A simple derivation of Stirling’s asymptotic series,” Amer. Math. Monthly, 93, 25–29 (1986).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Xiamen University, Xiamen, China

    X.-M. Zeng

Authors
  1. X.-M. Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 11, pp. 1570–1576, November, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zeng, XM. Approximation of absolutely continuous functions by stancu beta operators. Ukr Math J 63, 1787–1794 (2012). https://doi.org/10.1007/s11253-012-0614-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-012-0614-4

Keywords

Search

Navigation