Skip to main content
SpringerLink
Log in

Korovkin-Type Approximation Theorem for Double Sequences of Positive Linear Operators via Statistical A-Summability

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper, using the concept of statistical A-summability which is stronger than the A-statistical convergence we provide a Korovkin-type approximation theorem on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. We also study the rates of statistical A-summability of positive linear 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. DeVore, R.A.: The Approximation of Continuous Functions by Positive Linear Operators. Lecture Notes in Mathematics, vol. 293. Springer, Berlin (1972)

  2. Dirik F., Demirci K.: Korovkin type approximation theorem for functions of two variables in statistical sense. Turk. J. Math. 34, 73–83 (2010)

    MathSciNet  MATH  Google Scholar 

  3. Gadjiev A.D., Orhan C.: Some approximation theorems via statistical convergence. Rocky Mountain J. Math. 32, 129–138 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hamilton H.J.: Transformations of multiple sequences. Duke Math. J. 2, 29–60 (1936)

    Article  MathSciNet  Google Scholar 

  5. Hardy G.H.: Divergent Series. Oxford Univ. Press, London (1949)

    MATH  Google Scholar 

  6. Karakuş S., Demirci K., Duman O.: Equi-statistical convergence of positive linear operators. J. Math. Anal. Appl. 339, 1065–1072 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Korovkin P.P.: Linear Operators and Approximation Theory. Hindustan Publ. Co., Delhi (1960)

    Google Scholar 

  8. Moricz F.: Statistical convergence of multiple sequences. Arch. Math. (Basel) 81, 82–89 (2004)

    Article  MathSciNet  Google Scholar 

  9. Moricz F.: Tauberian theorems for double sequences that are statistically summable (C, 1, 1). J. Math. Anal. Appl. 286, 340–350 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mursaleen M., Edely O.H.H.: Statistical convergence of double sequences. J. Math. Anal. Appl. 288, 223–231 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Pringsheim A.: Zur theorie der zweifach unendlichen zahlenfolgen. Math. Ann. 53, 289–321 (1900)

    Article  MathSciNet  MATH  Google Scholar 

  12. Robison G.M.: Divergent double sequences and series. Am. Math. Soc. Transl. 28, 50–73 (1926)

    Article  MathSciNet  MATH  Google Scholar 

  13. Stancu D.D.: A method for obtaining polynomials of Bernstein type of two variables. Am. Math. Monthly 70(3), 260–264 (1963)

    Article  MathSciNet  Google Scholar 

  14. Volkov V.I.: On the convergence of sequences of linear positive operators in the space of two variables. Dokl. Akad. Nauk. SSSR (N.S.) 115, 17–19 (1957)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Sinop University, 57000, Sinop, Turkey

    Kamil Demirci & Sevda Karakuş

Authors
  1. Kamil Demirci
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sevda Karakuş
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sevda Karakuş.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Demirci, K., Karakuş, S. Korovkin-Type Approximation Theorem for Double Sequences of Positive Linear Operators via Statistical A-Summability. Results. Math. 63, 1–13 (2013). https://doi.org/10.1007/s00025-011-0140-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-011-0140-y

Mathematics Subject Classification (2010)

Keywords

Search

Navigation