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An extremal problem for polynomials with a prescribed zero. II


Authors: Q. I. Rahman and G. Schmeisser
Journal: Proc. Amer. Math. Soc. 73 (1979), 375-378
MSC: Primary 30A10; Secondary 26D05
DOI: https://doi.org/10.1090/S0002-9939-1979-0518524-4
MathSciNet review: 518524
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Abstract | References | Similar Articles | Additional Information

Abstract: Improving upon an earlier estimate it is shown that if $ {p_n}(z)$ is a polynomial of degree at most n such that $ {p_n}(1) = 0$ and $ {\max _{\vert z\vert = 1}}\vert{p_n}(z)\vert \leqslant 1$, then $ \vert{p_n}(0)\vert < 1 - (1.03369)/n + O(1/{n^2})$.


References [Enhancements On Off] (What's this?)

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  • [2] A. Giroux and Q. I. Rahman, Inequalities for polynomials with a prescribed zero, Trans. Amer. Math. Soc. 193 (1974), 67-98. MR 0352427 (50:4914)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0518524-4
Keywords: Extremal problem, polynomials with a prescribed zero
Article copyright: © Copyright 1979 American Mathematical Society

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