Skip to main content
Log in

MixedK-functionals: A measure of smoothness for blending-type approximation

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

References

  1. Badea, C., Badea, I., Cottin, C., Gonska, H.H.: Notes on the degree of approximation ofB-continuous andB-differentiable functions. J. Approx. Theory Appl.4, 95–108 (1988)

    MATH  MathSciNet  Google Scholar 

  2. Badea, C., Badea, I., Gonska, H.H.: A test function theorem and approximation by pseudopolynomials. Bull. Aust. Math. Soc.34, 53–64 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cottin, C.: Quantitative Aussagen zur Blending-Typ-Approximation. Dissertation, Universität Duisburg 1988

  4. Dahmen, W., DeVore, R.A., Scherer, K.: Multidimensional spline approximation. SIAM J. Numer. Anal.17, 380–402 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  5. DeVore, R.A.: Degree of approximation. In: Lorentz, G.G., Chui, C.K., Schumaker, L.L. (eds.) Approximation theory II. Proceedings Austin 1976, pp. 117–161. New York: Academic Press 1976

    Google Scholar 

  6. Gonska, H.H.: Quantitative Approximation inC(X). Habilitationsschrift, Universität Duisburg 1985

  7. Gonska, H.H.: Degree of simultaneous approximation of bivariate functions by Gordon operators. J. Approx. Theory (to appear)

  8. Gonska, H.H., Jetter, K.: Jackson-type theorems on approximation by trigonometric and algebraic pseudopolynomials. J. Approx. Theory48, 396–406 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gordon, W.J., Cheney, E.W.: Bivariate and multivariate interpolation with noncommutative projectors. In: Butzer, P.L., Sz.-Nagy, B. (eds.), Linear spaces and approximation. ISNM40, 381–387. Basel: Birkhäuser 1978

    Google Scholar 

  10. Haußmann, W., Jetter, K., Steinhaus, B.: Degree of best approximation by trigonometric blending functions. Math. Z.189, 143–150 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  11. Johnen, H.: Inequalities connected with the moduli of smoothness. Math. Vestnik9, 289–303 (1972)

    MathSciNet  Google Scholar 

  12. Johnen, H., Scherer, K.: On the equivalence of theK-functional and moduli of continuity and some applications. In: Schempp, W., Zeller, K. (eds.), Constructive theory of functions of several variables. (Lect. Notes Math., vol. 571, pp. 119–140) Berlin Heidelberg New York: Springer 1977

    Chapter  Google Scholar 

  13. Korneîčuk, N.P.: Extremal problems of approximation theory (Russian). Moskau: Izdat. “Nauka” 1976

    Google Scholar 

  14. Lorentz, G.G.: Approximation of functions. New York: Holt, Rinehart and Winston 1966

    MATH  Google Scholar 

  15. Mitjagin, B.S., Semenov, E.M.: Lack of interpolation of linear operators in spaces of smooth functions. Math. USSR, Izv.11, 1229–1266 (1977)

    Article  Google Scholar 

  16. Timan, A.F.: Theory of approximation of functions of a real variable. Oxford: Pergamon Press 1963

    MATH  Google Scholar 

  17. Schumaker, L.L.: Spline functions: basic theory. New York: Wiley & Sons 1981

    MATH  Google Scholar 

  18. Žuk, V., Natanson, G.: On the problem of approximating functions by means of positive operators (Russian). Tartu Riikl. Ül. Toimetised430, 58–69 (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cottin, C. MixedK-functionals: A measure of smoothness for blending-type approximation. Math Z 204, 69–83 (1990). https://doi.org/10.1007/BF02570860

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02570860

Keywords

Navigation