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Proceedings of the American Mathematical Society

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

 
 

 

Some inequalities for polynomials


Author: Q. I. Rahman
Journal: Proc. Amer. Math. Soc. 56 (1976), 225-230
MSC: Primary 30A08
DOI: https://doi.org/10.1090/S0002-9939-1976-0402016-4
MathSciNet review: 0402016
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Abstract: Let ${p_n}(z)$ be a polynomial of degree $n$. Given that ${p_n}(z)$ has a zero on the circle $|z| = \rho (0 < \rho < \infty )$ we estimate ${\max _{|z| = R > 1}}|{p_n}(z)|$ in terms of ${\max _{|z| = 1}}|{p_n}(z)|$. We also consider some other related problems.


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Keywords: Polynomials with a prescribed zero, Schwarz’s lemma
Article copyright: © Copyright 1976 American Mathematical Society