TY - JOUR
T1 - Asymptotic Property of Approximation to $x^α$sgn$x$ by Newman Type Operators
AU - Zhan , Qian
AU - Xu , Shusheng
JO - Communications in Mathematical Research 
VL - 3
SP - 193
EP - 199
PY - 2021
DA - 2021/05
SN - 27
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19082.html
KW - rational approximation, asymptotic property, Newman type operator.
AB - <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>