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# Bernstein type inequality in monotone rational approximation

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### Abstract

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.

### Author and article information

###### Journal
22 September 2010
###### Article
1009.4430