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Proceedings of the American Mathematical Society

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

 

 

A new proof and a generalization of a theorem of de Bruijn


Author: Abdul Aziz
Journal: Proc. Amer. Math. Soc. 106 (1989), 345-350
MSC: Primary 30A10; Secondary 26C05, 30C10
MathSciNet review: 933511
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Abstract: Using a recently developed interpolation formula, we present elementary new and simple proofs of De Bruijn's theorem and Zygmund's inequality concerning the integral mean estimates for polynomials. We also present a generalization of De Bruijn's theorem which leads to a refinement of a theorem of Erdös and Lax.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0933511-6
Keywords: Derivative of a polynomial, integral mean estimates, inequalities in the complex domain, self-inversive polynomials
Article copyright: © Copyright 1989 American Mathematical Society