Skip to main content
Log in

Statistical approximation properties of q-Baskakov-Kantorovich operators

  • Research Article
  • Published:
Central European Journal of Mathematics

Abstract

In the present paper we introduce a q-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < q < 1.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abel U., Gupta V., An estimate of the rate of convergence of a Bezier variant of the Baskakov-Kantorovich operators for bounded variation functions, Demonstratio Math., 2003, 36, 123–136

    MATH  MathSciNet  Google Scholar 

  2. Agratini O., On statistical approximation in spaces of continuous functions, Positivity, 2009, 13, 735–743

    Article  Google Scholar 

  3. Andrews G.E., Askey R., Roy R., Special functions, Cambridge Univ. Press., 1999

  4. Aral A., Gupta V., On the Durrmeyer type modification of the q-Baskakov type operators, Nonlinear Anal., (in press), DOI: 10.1016/j.na.2009.07.052

  5. Baskakov V.A., An example of a sequence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk. SSSR, 1957, 113, 249–251 (in Russian)

    MATH  MathSciNet  Google Scholar 

  6. Derriennic M.-M., Modified Bernstein polynomials and Jacobi polynomials in q-calculus, Rend. Circ. Mat. Palermo Serie II, 2005, 76, 269–290

    MathSciNet  Google Scholar 

  7. Doǧru O., Duman O., Statistical approximation of Meyer-König and Zeller operators based on q-integers, Publ. Math. Debrecen, 2006, 68, 199–214

    MathSciNet  Google Scholar 

  8. Dogru O., Duman O., Orhan C., Statistical approximation by generalized Meyer-König and Zeller type operators, Studia Sci. Math. Hungar., 2003, 40, 359–371

    MATH  MathSciNet  Google Scholar 

  9. Dogru O., Gupta V., Monotonicity and the asymptotic estimate of Bleimann Butzer and Hahn operators based on q-integers, Georgian Math. J., 2005, 12, 415–422

    MATH  MathSciNet  Google Scholar 

  10. Doǧru O., Gupta V., Korovkin-type approximation properties of bivariate q-Meyer-König and Zeller operators, Calcolo, 2006, 43, 51–63

    Article  MathSciNet  Google Scholar 

  11. Duman O., Orhan C., Statistical approximation by positive linear operators, Studia Math., 2006, 161, 187–197

    Article  MathSciNet  Google Scholar 

  12. Ernst T., The history of q-calculus and a new method, U.U.D.M. Report 2000, 16, Uppsala, Departament of Mathematics, Uppsala University, 2000

  13. Gupta V., Some approximation properties of q-Durrmeyer operators, Appl. Math. Comput., 2008, 197, 172–178

    Article  MATH  MathSciNet  Google Scholar 

  14. Kac V., Cheung P., Quantum calculus, Universitext, Springer-Verlag, New York, 2002

    Google Scholar 

  15. López-Moreno A.-J., Weighted silmultaneous approximation with Baskakov type operators, Acta Math. Hungar., 2004, 104, 143–151

    Article  MATH  MathSciNet  Google Scholar 

  16. Lorentz G.G., Bernstein polynomials, Math. Expo. Vol. 8, Univ. of Toronto Press, Toronto, 1953

    Google Scholar 

  17. Phillips G.M., Bernstein polynomials based on the q-integers, Ann. Numer. Math., 1997, 4, 511–518

    MATH  MathSciNet  Google Scholar 

  18. Radu C., Statistical approximation properties of Kantorovich operators based on q-integers, Creat. Math. Inform., 2008, 17, 75–84

    MathSciNet  Google Scholar 

  19. Trif T., Meyer-König and Zeller operators based on the q-integers, Rev. Anal. Numér. Théor. Approx., 2000, 29, 221–229

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vijay Gupta.

About this article

Cite this article

Gupta, V., Radu, C. Statistical approximation properties of q-Baskakov-Kantorovich operators. centr.eur.j.math. 7, 809–818 (2009). https://doi.org/10.2478/s11533-009-0055-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11533-009-0055-y

MSC

Keywords

Navigation