Skip to main content
Log in

Approximation by Kantorovich-Bernstein polynomials inL p(0<p<1)-metric

  • Published:
Approximation Theory and its Applications

Abstract

The purpose of the present paper is to evaluate the error of the approximation of the function f∈L1[0,1] by Kantorovich-Bernstein polynomials in Lp-metric (0<p<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. De Vore, R.A. and Popov, V.A., Interpolation of Besov Spaces, Trans. of Amer. Math. Soc., 305 (1988), 397–414.

    Article  Google Scholar 

  2. Ditzian, Z. and Zhou, X., Kantorovich-Bernstein Polynomials, Constr. Approx., 6 (1990), 421–435.

    Article  MATH  MathSciNet  Google Scholar 

  3. Ivanov, K. G., On a New Characteristic of Functions I, Serdica, 8 (1982), 262–279.

    MATH  MathSciNet  Google Scholar 

  4. Ivanov, K. G., Approximation by Bernstein Polynomials inL p Metric, Constructive theory of functions′84, Sofia, 1984, 421–429.

  5. Ivanov, K. G., Converse Theorem for Approximation by Bernstein Polynomials inL p [0, 1] (1<p <∞), Constr. Approx., 2 (1986), 377–392.

    Article  MATH  MathSciNet  Google Scholar 

  6. Maier, V., TheL 1 Saturation Class of the Kantorovich Operator, J. Approx. Theory, 22 (1978), 223–232.

    Article  MATH  MathSciNet  Google Scholar 

  7. Petrushev, P. P., and Popov, V. A., Rational Approximation of Real Functions, Cambridge University Press, Enciclopedia of Mathematics and its Applications, 28 (1987).

  8. Riemenschneider, S. D., TheL p Saturation of Kantorovich-Bernstein Polynomials, J. Approx. Theory, 23 (1978), 158–162.

    Article  MATH  MathSciNet  Google Scholar 

  9. Sendov, Bl., and Popov, V., Averaged Moduli of Smoothness, Sofia, 1983.

  10. Storozenko, E. A. and Oswald, P., Moduli of Smoothness and Best Approximation in the SpacesL p, 0<p<1, Anal. Math., 3 (1977), 141–150.

    Article  MathSciNet  Google Scholar 

  11. Tachev, G. T., Converse Theorem for the Best Algebraic Approximation inL p[−1,1],0<p<1, Serdica, 1990, to appear.

  12. Tachev, G. T., Direct Estimation for Approximation by Bernstein Polynomials inL p[0,1],0<p<1, Math. Balk., 3 (1989) 51–60.

    MATH  MathSciNet  Google Scholar 

  13. Totik, V.,L p(p>1) Approximation by Kantorovich Ploynomials, Analysis, 3 (1983), 79–100.

    MATH  MathSciNet  Google Scholar 

  14. Totik, V., An Interpolation Theory and its Applications to Positive Operatovrs, Pacific J. Math., 111 (1984), 447–481.

    MATH  MathSciNet  Google Scholar 

  15. Totik, V., The Necessity of a New Kind of Modulus of Smoothness, ISNM, 65 (1984), 233–247.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tachev, G.T. Approximation by Kantorovich-Bernstein polynomials inL p(0<p<1)-metric. Approx. Theory & its Appl. 8, 38–50 (1992). https://doi.org/10.1007/BF02836337

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02836337

Keywords

Navigation