Sign-Preserving Approximation of Periodic Functions
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.
English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 8, pp 1314-1328.
Citation Example: Pleshakov M. G., Popov P. A. Sign-Preserving Approximation of Periodic Functions // Ukr. Mat. Zh. - 2003. - 55, № 8. - pp. 1087-1098.