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Integral Mean Estimates for Polynomials whose Zeros are within a Circle  
 
  Authors: K. K. Dewan, Naresh Singh, Barchand Chanam, Abdullah Mir,  
  Keywords: Polynomials, Zeros of order $m$, Inequalities, Polar derivatives.  
  Date Received: 17/10/07  
  Date Accepted: 19/12/08  
  Subject Codes:

30A10, 30C10, 30D15

  
  Editors: Gradimir V. Milovanovic,  
 
  Abstract:

Let $ p(z)$ be a polynomial of degree $ n$. Zygmund [11] has shown that for

In this paper, we have obtained inequalities in the reverse direction for the polynomials having a zero of order $ m$ at the origin. We also consider a problem for the class of polynomials $ p(z)=a_nz^n +\sum\limits_{\nu=\mu}^n a_{n-\nu}z^{n-\nu}$ not vanishing outside the disk , $ k\le 1$ and obtain a result which, besides yielding some interesting results as corollaries, includes a result due to Aziz and Shah [Indian J. Pure Appl. Math., 28 (1997), 1413-1419] as a special case. ;


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