On the Bernstein's constant in convex approximation

Sorin Gal

Abstract


Original proposers of the open problem: Sorin G. Gal
The year when the open problem was proposed: 2009
Sponsor of the submission: Heiner Gonska - University of Duisburg-Essen
AMS Subject classification: 41
Status of the problem: Open


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 $\lambda \ge 1$.

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