On the degree of piecewise shape-preserving approximation by polynomials

We show that the degree of piecewise qq-coconvex approximation En(q)(f,Ys) of a qq-convex function by algebraic polynomials of degree 1,N=s+2,q=1, and α>2,N=s+3,q=2 complement earlier results on comonotone and coconvex approximation by polynomials respectively.