Skip to main content
SpringerLink
Log in

Local Approximation Properties of Modified Baskakov Operators

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we introduce a general modification of the classical Baskakov operators which do not need to preserve the test function x 2. Then, we study an approximation theorem, a Voronovskaya theorem, and various local approximation results for our modified Baskakov 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. Agratini, O.: Linear operators that preserve some test functions. Int. J. Math. Math. Sci. Art.ID 94136, 11 pp (2006)

    Google Scholar 

  2. Agratini O.: On the iterates of a class of summation-type linear positive operators. Comput. Math. Appl. 55, 1178–1180 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Altomare F., Campiti M.: Korovkin-type Approximation Theory and its Application. Walter de Gruyter Studies in Math. 17. de Gruyter & Co., Berlin (1994)

    Google Scholar 

  4. Baskakov V.A.: An instance of a sequence of linear positive operators in the space of continuous functions. Dokl. Akad. Nauk. SSSR (N.S.) 113, 249–251 (1957)

    MATH  MathSciNet  Google Scholar 

  5. DeVore R.A., Lorentz G.G.: Constructive Approximation. Springer-Verlag, Berlin (1993)

    MATH  Google Scholar 

  6. Duman, O., Özarslan, M.A.: Global approximation results for modified Szász-Mirakjan operators. Taiwan. J. Math. (accepted)

  7. Duman, O., Özarslan, M.A.: Szász-Mirakjan type operators providing a better error estimation. Appl. Math. Lett. 20, 1184–1188 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  8. Duman O., Özarslan M.A., Aktuğlu H.: Better error estimation for Szász- Mirakjan-Beta operators. J. Comput. Anal. Appl. 10, 53–59 (2008)

    MATH  MathSciNet  Google Scholar 

  9. King J.P.: Positive linear operators which preserve x 2. Acta. Math. Hungar. 99, 203–208 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Mahmudov N.I.: Korovkin-type theorems and applications. Cent. Eur. J. Math. 7, 348–356 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Özarslan M.A., Duman O.: Local approximation results for Szász-Mirakjan type operators. Arch. Math. (Basel) 90, 144–149 (2008)

    MATH  MathSciNet  Google Scholar 

  12. Özarslan M.A., Duman O.: MKZ type operators providing a better estimation on [1/2,1). Can. Math. Bull. 50, 434–439 (2007)

    Article  MATH  Google Scholar 

  13. Rempulska L., Tomczak K.: Approximation by certain linear opereators preserving x 2. Turk. J. Math. 33, 273–281 (2009)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Mersin 10, Gazimagusa, Turkey

    M. Ali Özarslan & Nazım I. Mahmudov

  2. Department of Mathematics, Faculty of Arts and Sciences, TOBB Economics and Technology University, Söğütözü, 06530, Ankara, Turkey

    Oktay Duman

Authors
  1. M. Ali Özarslan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oktay Duman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nazım I. Mahmudov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Ali Özarslan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Özarslan, M.A., Duman, O. & Mahmudov, N.I. Local Approximation Properties of Modified Baskakov Operators. Results. Math. 59, 1–11 (2011). https://doi.org/10.1007/s00025-010-0045-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-010-0045-1

Mathematics Subject Classification (2010)

Keywords

Search

Navigation