  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 $\lambda
\ge 1$.
