On the Bernstein's constant in convex approximation

Abstract

Denoting by $E_n^{(+2)}(f)$ the best uniform approximation of $f$ by convex polynomials of degree $\le n$, there is an open question if there exists the limit ${\lim }_{n\to \infty }{n}^{\lambda }{E}_n^{(+2)}(|x{|}^{\lambda })$ for $\lambda \ge 1$.

On the first line of Open Question 2, "[-1, 1]" was replaced by "R" . All the rest remain unchanged