Generalization of Negative Results for Interpolation Convex Approximation of Functions Having a Fractional Derivative in Sobolev Space

We discuss whether on not it is possible to have interpolatory estimates in the approximation of a function Sobolev`s space by polynomials. The prob-lem positive estimate pointwise degree approxi-mation r times continuously differentiable and func-tions [0, 1]. Estimates form (1) for are known ([1, 2]). problem monotone that estimating de-gree nondecreasing bymonotone were proved [3, 4, 7]. In 4] consider natural equal one. [7] real rmore two. It was fails more convex ap-proximation con-vex [8-10]. [8] [9] [10] question algebraic polynomial consider, if index Sobolev interval from three four. gen-eralizes false This paper investigates issue functions polynomials two three.Similarly [10], counterexample built, which shows generalizes false.This isthe generalization results papers [11]. main result analog theorem 2.3