Coconvex polynomial approximation Original Research Article

Let f∈C[−1,1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are coconvex with it, namely, polynomials and piecewise polynomials that change their convexity exactly at the points where f does. We obtain Jackson-type estimates and summarize the positive and negative results in a truth-table as we have previously done for comonotone approximation.