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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Inequalities for the derivative of a polynomial


Author: Abdul Aziz
Journal: Proc. Amer. Math. Soc. 89 (1983), 259-266
MSC: Primary 30C10; Secondary 26D05
DOI: https://doi.org/10.1090/S0002-9939-1983-0712634-5
MathSciNet review: 712634
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Abstract: Let $ P(z) = \sum\nolimits_{j = 0}^n {{a_j}{z^j} = c\prod\nolimits_{j = 1}^n {(z - {z_j})} } $ be a polynomial of degree $ n$ and $ P'(z)$ its derivative. In this paper we consider the problem of estimating the maximum of $ \left\vert {P'(z)} \right\vert$ on $ \left\vert z \right\vert = 1$ under some assumptions on the zeros or on the coefficients of $ P(z)$ and obtain certain sharp results.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0712634-5
Keywords: Derivative of a polynomial, inequalities in the complex domain, self-inversive polynomials
Article copyright: © Copyright 1983 American Mathematical Society