Sign-Preserving Approximation of Periodic Functions - Pleshakov, M. G.; Popov, P. A. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
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