Linear Combinations of Bernstein Polynomials

If f(x) is denned on [0, 1], then its corresponding Bernstein polynomial approaches f(x) uniformly on [0, 1], if f(x) is continuous on [0, 1]. If f(x) is bounded on [0, 1], then at every point x where the second derivative exists (Voronowskaja [7], see also [5])