On Exact Estimates for the Pointwise Approximation of the Classes $W^rH^ω$ by Algebraic Polynomials

Abstract

We obtain estimates for the approximation of functions of the class W ^r H ^ω, where ω(t) is a convex modulus of continuity such that tω′(t) does not decrease, by algebraic polynomials with regard for the position of a point on the segment [−1, 1]. The estimates obtained cannot be improved for all moduli of continuity simultaneously.