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Volume 10, Issue 1, Article 23 |
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Integral Mean Estimates for Polynomials whose Zeros are within a Circle
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Authors: |
K. K. Dewan, Naresh Singh, Barchand Chanam, Abdullah Mir, |
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Keywords:
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Polynomials, Zeros of order $m$, Inequalities, Polar derivatives. |
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Date Received:
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17/10/07 |
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Date Accepted:
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19/12/08 |
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Subject Codes: |
30A10, 30C10, 30D15
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Editors: |
Gradimir V. Milovanovic, |
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Abstract: |
Let  be a polynomial of degree  . 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  at the origin. We also consider a problem for the class of polynomials  not vanishing outside the disk  ,  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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