JIPAM

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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