Skip to main content
Log in

Korovkin type approximation theorems on the space of continuously differentiable fnctions

  • Published:
Approximation Theory and its Applications

Abstract

It is studied Korovkin type approximation theorems on C(1) ([0, 1]) the space of continuously differentiable functions on the unit interval. It is proved that test functions for which Korovkin type approximation theorems hold depending on norms of C(1) ([0, 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. Altomare, F. and Baccaccio, C., On Korovkin-type Theorems in Spaces of Continuous Complex-valued Functions, Boll. Un. Mat. Ital. 6 (1982), No. 1, 75–86.

    Google Scholar 

  2. Altomare, F. and Campiti, M., Korovkin-Type Approximation Theorey and its Applications, de Gruyter, Berlin and New York, 1994.

    Google Scholar 

  3. Altomare, F. and Rosa, I., Approximation by Positive Operators in the SpaceC (p) ([a, b]), Anal. Numér. Théor. Approx., 18 (1989), 1–11.

    MATH  MathSciNet  Google Scholar 

  4. Berens, H. and Lorentz, G. G., Geometric Theory of Korovkin Sets, J. Approx. Theory, 15 (1975), 161–1189.

    Article  MATH  MathSciNet  Google Scholar 

  5. Brosowski, B., A Korovkin-type Theorem for Differentiable Functions, in Approximation TheoryI, ed. E. W. Cheney, Academic Press, 1980, 255–260.

  6. Izuchi, K., Takagi, H. and Watanabe, S., Sequential BKW-Operators and Function Algebras, J. Approx. Theory, 85 (1996), 185–200.

    Article  MATH  MathSciNet  Google Scholar 

  7. Knoop, H. B. and Pottinger, P., Ein Satz vom Korovkin-Type für Ck-Räume, Math. Z., 148 (1976), 23–32.

    Article  MATH  MathSciNet  Google Scholar 

  8. Korovkin, P. P., On Convergence of Linear Operators in the Space of Continuous Functions, Dokl. Adad. Nauk. SSSR (N. S>), 90 (1953), 961–964. [In Russian].

    MATH  MathSciNet  Google Scholar 

  9. Korovkin, P. P., Linear Operators and Approximation Theory, Hindustan Publishing, Delhi, 1960

    Google Scholar 

  10. Matsumoto, T. and Watanabe, S., Extreme Points and Linear Isometries of the Domain of a Closed-derivation inC(K), J. Math. Soc. Japan, 48 (1996), 229–254.

    Article  MATH  MathSciNet  Google Scholar 

  11. Šaškin, Y. A., On Convergence of Contraction Operators, Math. Cluj., 11 (1969), 355–360.

    Google Scholar 

  12. Takahasi, S. E.,(T, E)-Korovkin Closures in Normed Spaces and BKW-operators, J. Approx. Theory, 82 (1995), 340–351.

    Article  MATH  MathSciNet  Google Scholar 

  13. Ustinov, G. M. and Vasil'čenko, A. A., Convergence of Operators in the Space of Differentiable Functions, Ural. Gos. Univ. Mat. Zap., 10 (1977), 8–14 [in Russian].

    MathSciNet  Google Scholar 

  14. Wulbert, D. E., Convergence of Operators and Korovkin’s Theorem, J. Approx. Theory 1 (1968), 381–390.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hirasawa, G., Izuchi, K. & Watanabe, S. Korovkin type approximation theorems on the space of continuously differentiable fnctions. Approx. Theory & its Appl. 16, 19–27 (2000). https://doi.org/10.1007/BF02837389

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02837389

Keywords

Navigation