@Article{CMR-27-3,
author = {Zhan, Qian and Xu, Shusheng},
title = {Asymptotic Property of Approximation to $x^α$sgn$x$ by Newman Type Operators},
journal = {Communications in Mathematical Research },
year = {2011},
volume = {27},
number = {3},
pages = {193--199},
abstract = {<p style="text-align: justify;">The approximation of $|x|$ by rational functions is a classical rational
problem. This paper deals with the rational approximation of the function $x^α$sgn$x$,
which equals $|x|$ if $α = 1$. We construct a Newman type operator $r_n(x)$ and show $$\mathop{\rm min}\limits_{|x|≤1} \{|x^α{\rm&nbsp;sgn}x − r_n(x)| \} ∼ Cn^{−\frac{α}{2}}e^{−\sqrt{2nα}},$$ where $C$ is a constant depending on $α$.</p>},
issn = {2707-8523},
doi = {https://doi.org/2011-CMR-19082},
url = {https://global-sci.com/article/81869/asymptotic-property-of-approximation-to-xasgnx-by-newman-type-operators}
}