Lobachevskii Journal of Mathematics

, Volume 34, Issue 3, pp 272–281 | Cite as

Approximation by the Durrmeyer-Baskakov-Stancu operators

  • Vishnu Narayan Mishra
  • Prashantkumar Patel


In the present paper we propose the Durrmeyer-Baskakov-Stancu operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0,∞). Also, Voronovskaja type theorem is studied.

Keywords and phrases

Durrmeyer type operators Weighted approximation Rate of convergence Stancu operators Modulus of continuities 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Sahai and G. Prasad, J. of Approximation Theory 45, 122 (1985).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    D. D. Stancu, Rev. Roumaine Math. Pure Appl. 13, 1173 (1968).MathSciNetzbMATHGoogle Scholar
  3. 3.
    D. D. Stancu, Calcolo 20(2), 211 (1983).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    S. N. Berstien, Commun. Soc. Math. Kharkow 13(2), 1 (1912).Google Scholar
  5. 5.
    B. Ibrahim, Comput. Math. Appl. 59, 274 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    R.A. DeVore and G. G. Lorentz, Constructive Approximation (Springer, Berlin, 1993).CrossRefzbMATHGoogle Scholar
  7. 7.
    A. D. Gadzhiev, Math Notes, 20(5–6), 996 (1976).Google Scholar
  8. 8.
    A. D. Gadjiev, R. O. Efendiyev, and E. Ibikli, Czechoslovak Math. J. 1(128), 45 (2003).MathSciNetCrossRefGoogle Scholar
  9. 9.
    J. P. King, Acta. Math. Hungar. 99, 203 (2003).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Z. Finta and V. Gupta, South East Asian Bull. Math. 6, 1037 (2008).MathSciNetGoogle Scholar
  11. 11.
    N. K. Govil and V. Gupta, Nonlinear Anal. 69(11), 3795 (2008).MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    I. Yksel and N. Ispir, Comput. Math. Appl. 52, 1463 (2006).MathSciNetCrossRefGoogle Scholar
  13. 13.
    G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, vol. 35 (Cambridge University Press, Cambridge, UK, 1990).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Department of Applied Mathematics and HumanitiesSardar Vallabhbhai National Institute of TechnologySurat(Gujarat), India

Personalised recommendations