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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.

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          Author and article information

          Journal
          22 September 2010
          Article
          1009.4430

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          East J. Approx. 11 (2005), no. 1, 103--108
          9 pages
          math.NA

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