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  Volume 6, Issue 4, Article 109
 
Another Refinement of Bernstein's Inequality
    Authors: Clément Frappier,  
    Keywords: Bernstein's inequality, Unit circle, Convolution method.  
    Date Received: 31/05/05  
    Date Accepted: 18/08/05  
    Subject Codes:

26D05, 26D10, 33A10.

  
    Editors: Narendra K. Govil,  
 
    Abstract:

Given a polynomial $ p(z) = sum_{j=0}^n a_j z^j$, we denote by $ Vert Vert$ the maximum norm on the unit circle $ {z colon vert zvert = 1}$. We obtain a characterization of the best possible constant $ x_n ge frac{1}{2}$ such that the inequality $ Vert zp'(z) - xa_n z^n Vert le (n-x)Vert pVert$ holds for $ 0 le x le x_n$.

         
       
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