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Ukrainian Mathematical Journal

, Volume 55, Issue 8, pp 1314–1328 | Cite as

Sign-Preserving Approximation of Periodic Functions

  • M. G. Pleshakov
  • P. A. Popov
Article

Abstract

We prove the Jackson theorem for a zero-preserving approximation of periodic functions (i.e., in the case where the approximating polynomial has the same zeros yi) and for a sign-preserving approximation [i.e., in the case where the approximating polynomial is of the same sign as a function f on each interval (yi, yi − 1)]. Here, yi are the points obtained from the initial points −π ≤ y2sy2s−1 <...< y1 < π using the equality yi = yi + 2s + 2π furthermore, these points are zeros of a 2π-periodic continuous function f.

Keywords

Continuous Function Initial Point Periodic Function Jackson Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2003

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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