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$L_p$ Inequalities for the Polar Derivative of a Polynomial  
 
  Authors: Nisar A. Rather,  
  Keywords: $L_p$ inequalities, Polar derivatives, Polynomials.  
  Date Received: 04/05/07  
  Date Accepted: 30/07/08  
  Subject Codes:

26D10, 41A17.

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

Let $ D_{lpha}P(z)$ denote the polar derivative of a polynomial $ P(z)$ of degree $ n$ with respect to real or complex number $ lpha$. If $ P(z)$ does not vanish in $ ert zert< k, kgeq1$, then it has been proved that for $ ertlphaertgeq1$ and $ p> 0$,

$displaystyle leftVert D_{lpha}PightVert _{p}leqleft( frac{leftert... ...leftVert k+zightVert _{p}}ight) leftVert PightVert _{p}smallskip .$    

An analogous result for the class of polynomials having no zero in $ leftert zightert>k,kleq1$ is also obtained. ;


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