Higher order derivatives of approximation polynomials on $\mathbb{R}$

Abstract

D. Leviatan has investigated the behavior of the higher order derivatives of approximation polynomials of the differentiable function $f$ on $[-1,1]$. Especially, when $P_n$ is the best approximation of $f$, he estimates the differences $\Vert f^{(k)}-P_n^{(k)}{\Vert }_{L_{\infty }([-1,1])}$, $k=0,1,2,...$. In this paper, we give the analogies for them with respect to the differentiable functions on $\mathbb{R}$, and we apply the result to the monotone approximation.

References in corpus (1)

• The de la Vallee Poussin mean and polynomial approximation for exponential weight