Positive results and counterexamples in comonotone approximation II

Let En(f)En(f) denote the degree of approximation of f∈C[−1,1]f∈C[−1,1], by algebraic polynomials of degree 0α>0 and N≥2N≥2, nαEn(f)≤1,n≥N. Suppose that ff changes its monotonicity s≥1s≥1 times in [−1,1][−1,1]. We are interested in what may be said about its degree of approximation by polynomials of degree