Optimal interpolation with polynomials having fixed roots (Q1107753)

The author investigates optimal interpolation of potor transforms every continuous, n-convex function into an r-convex function. Their proof is based on the fact that the Bernstein polynomials of a continuous, n- convex function F (which converges uniformly to F) are themselves n- convex. We express the result of Bojanic and Roulier in a slightly different notation and terminology and then we take a similar approach, after obtaining various decompositions of an n-convex function, to obtain new sufficient conditions that a continuous linear operator transforms every continuous n-convex function into an r-convex function.