Bernstein type inequality in monotone rational approximation

Details Bernstein type inequality in monotone rational approximation Bernstein type inequality in monotone rational approximation

2010-09-22

arxiv.org/abs/1009.4430v1

East J. Approx. 11 (2005), no. 1, 103--108

Mathematics

Numerical Analysis

9 pages

Scientific paper

The following analog of Bernstein inequality for monotone rational functions
is established: if $R$ is an increasing on $[-1,1]$ rational function of degree
$n$, then $$ R'(x)<\frac{9^n}{1-x^2}\|R\|,\quad x\in (-1,1). $$ The exponential
dependence of constant factor on $n$ is shown, with sharp estimates for odd
rational functions.

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