| Abstract: | It is well-known that in two or more variables Bernstein polynomials do not preserve convexity. Here we present two variations, one stronger than the classical notion, the other one weaker, which are preserved and do coincide with classical convexity in the univariate case. Moreover, it will be shown that even the weaker notion is sufficient for the monotonicity of successive Bernstein polynomials, strengthening the well-known result that monotonicity holds for classically convex functions. |
