Sign-Preserving Approximation of Periodic Functions

  • M. G. Pleshakov
  • P. A. Popov


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 y i) 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 (y i, y i − 1)]. Here, y i are the points obtained from the initial points −π ≤ y 2s y 2s−1 <...< y1 < π using the equality yi = yi + 2s + 2π furthermore, these points are zeros of a 2π-periodic continuous function f.
How to Cite
Pleshakov, M. G., and P. A. Popov. “Sign-Preserving Approximation of Periodic Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 55, no. 8, Aug. 2003, pp. 1087-98,
Research articles