Skip to main content
SpringerLink
Log in

Coconvex approximation of continuous functions

  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

Suppose thatf(x)∈C[−1, 1],f(x) is convex in [0,1] and concave in [−1,0] with the new concept of regular convexity-turning points,we obtain the following estimates of Jackson type for coconvex approximation off(x) by algebraic polynomials of degree ⩽n:

$$\tilde E_n (f) \leqslant C \omega \left( {f, \frac{1}{n}} \right)$$

.

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., Monotone approximation by polynomials,SIAM J. Math. Anal.,8(1977), 906–921.

    Article  Google Scholar 

  2. Shvedov, A.S., Orders of coapproximation of functions by algebraic polynomials,Matem. Zametki,30(1981), 117–130.

    Google Scholar 

  3. Yu Xiangming and Ma Yongpei, Generalized monotone approximation inL p space,Acta Mathematica Sinica, New Series,5 (1989), 48–56.

    Google Scholar 

  4. Yu Xiangming, On comonotone approximation and coconvex approximation of differentiable functions, to appear.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University, China

    Yu Xiangming

Authors
  1. Yu Xiangming
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project Supported by the Science Fund of the Chinese Academy of Sciences.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xiangming, Y. Coconvex approximation of continuous functions. Acta Mathematica Sinica 6, 220–229 (1990). https://doi.org/10.1007/BF02108201

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02108201

Keywords

Search

Navigation