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arXiv · 1403.0477

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

Hee Sun Jung·Ryozi Sakai
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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 $\|f^{(k)}-P_n^{(k)}\|_{L_\infty([-1,1])}$, $k=0,1,2,...$. 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.

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Hee Sun Jung, Ryozi Sakai. 2014-02-27. Higher order derivatives of approximation polynomials on $\mathbb{R}$. https://arxiv.org/abs/1403.0477

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