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On approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces

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Analysis in Theory and Applications

Abstract

This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f (x) ∈ LM* [0,1], changes its sign at most once in (0,1), then there exists x0 ∈ (0,1) and a polynomial Pn ∈ Πn(+) such that

$$\parallel f(x) - \frac{{x - x_0 }}{{P_n (x)}}\parallel _M \leqslant C\omega (f,n^{ - \frac{1}{2}} )_M ,$$

where Πn(+) indicates the set of all polynomials of degree n with positive coefficients.

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References

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Authors and Affiliations

  1. Inner Mongolia Normal University, Huhhot, China

    Xiaoli Wang & Garidi Wu

  2. Inner Mongolia Agriculture University, Huhhot, China

    Ran Huo

  3. Department of Mathematics, Inner Mongolia Normal University, Huhhot, 010022, P. R. China

    Xiaoli Wang & Garidi Wu

  4. Department of Science, Inner Mongolia Agriculture University, Huhhot, 010022, P. R. China

    Ran Huo

Authors
  1. Xiaoli Wang
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  2. Ran Huo
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  3. Garidi Wu
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Correspondence to Xiaoli Wang.

Additional information

Supported by Inner Mongolia Natural Science Foundations of China (200408020108).

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Wang, X., Huo, R. & Wu, G. On approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces. Anal. Theory Appl. 24, 364–376 (2008). https://doi.org/10.1007/s10496-008-0364-1

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  • DOI: https://doi.org/10.1007/s10496-008-0364-1

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