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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the derivative with respect to a point


Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 101 (1987), 327-330
MSC: Primary 30C15
MathSciNet review: 902551
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Abstract: The derivative of a polynomial $ p(z)$ with respect to a point $ \varsigma $ is defined by the formula $ {A_\varsigma }p(z) = (\varsigma - z)p'(z) + np(z)$, where $ n$ is the degree of the polynomial. Let $ p(z)$ have all its zeros in the unit disk and one zero at $ z = 1$. We determine a minimal region that must contain at least one zero of $ {A_\varsigma }p(z)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0902551-3
PII: S 0002-9939(1987)0902551-3
Keywords: Polynomials, zeros of the derivative, derivative with respect to a point, minimal set
Article copyright: © Copyright 1987 American Mathematical Society