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

DOI:
https://doi.org/10.1090/S0002-9939-1989-0933511-6

MathSciNet review:
933511

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

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