INTERPOLATORY ESTIMATES IN MONOTONЕ PIECEWISE–POLYNOMIAL APPROXIMATION

Abstract

Recently we obtained an interpolation estimate for a monotonе piecewise-polynomial approximation of a continuous on a segment function, involving the second modulus of continuity of the r-th derivative, and also have shown that this estimate is valid only for a sufficiently large number of segments of the partition, which essentially depends on the function. In paper [2] both results are widespread to the case of a convex approximation and obtained in somewhat more preciseform. We show that in the case of a monotone approximation, the corresponding results are also valid in an appropriate more precise form.