Ukrainian Mathematical Journal

, Volume 56, Issue 1, pp 153–160 | Cite as

Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions

  • M. G. Pleshakov
  • P. A. Popov


We consider a 2π-periodic function f continuous on \(\mathbb{R}\) and changing its sign at 2s points yi ∈ [−π, π). For this function, we prove the existence of a trigonometric polynomial Tn of degree ≤n that changes its sign at the same points yi and is such that the deviation | f(x) − Tn(x) | satisfies the second Jackson inequality.


Periodic Function Jackson Inequality 
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  1. 1.
    M. G. Pleshakov and P. A. Popov, “Sign-preserving approximation of periodic functions,” Ukr. Mat. Zh., 55, No. 8, 1087–1098 (2003).Google Scholar
  2. 2.
    I. A. Shevchuk, Polynomial Approximation and Traces of Functions Continuous on an Interval [in Russian], Naukova Dumka, Kiev (1992).Google Scholar
  3. 3.
    M. G. Pleshakov, Comonotone Approximation of Periodic Functions from Sobolev Classes [in Russian], Candidate-Degree Thesis (Physics and Mathematics), Saratov (1998).Google Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • M. G. Pleshakov
    • 1
  • P. A. Popov
    • 2
  1. 1.Saratov UniversitySaratovRussia
  2. 2.Kiev National University of Technology and DesignKiev

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