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  Volume 5, Issue 1, Article 7
Note On Bernstein's Inequality For The Third Derivative Of A Polynomial

    Authors: Clément Frappier,  
    Keywords: Bernstein's inequality, Unit circle.  
    Date Received: 05/11/03  
    Date Accepted: 13/02/04  
    Subject Codes:

26D05, 26D10, 30A10

    Editors: Ram N. Mohapatra,  

Given a polynomial $ p(z)=\sum_{j=0}^n a_j z^j$, we give the best possible constant $ c_3(n)$ such that $ \Vert p^{\prime\prime\prime}\Vert + c_3(n) \vert a_0\vert \le n(n-1)(n-2)\Vert p\Vert$, where $ \Vert  \Vert$ is the maximum norm on the unit circle $ % \{ z : \vert z\vert = 1\}$. Most of the computations are done with a computer.

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