Some positive results and counterexamples in comonotone approximation
Let \(f\) be a continuous function on \([-1,1]\), which changes its monotonicity \(s\) times in the interval. This paper proves the validity of the Jackson-type estimates for the approximation of \(f\) by algebraic polynomials that are comonotone with it involving the Ditzian-Totik modules of continuity and a constant that depends only on \(s\). This paper also shows by counterexamples that in many cases this is not so, even for functions which possess locally absolutely continuous derivatives.
scientific article; zbMATH DE number 1019190
scientific article