A new proof and a generalization of a theorem of de Bruijn-Reference-Cited by-同舟云学术

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

Published:1989 Issue:2 Volume:106 Page:345-350
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Aziz Abdul

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1989-106-02/S0002-9939-1989-0933511-6/S0002-9939-1989-0933511-6.pdf

Reference7 articles.

1. Simple proof of a theorem of Erdős and Lax;Aziz, Abdul;Proc. Amer. Math. Soc.,1980

2. Inequalities concerning polynomials in the complex domain;de Bruijn, N. G.;Nederl. Akad. Wetensch., Proc.,1947

3. An inequality for self-inversive polynomials;Dewan, K. K.;J. Math. Anal. Appl.,1983

4. Proof of a conjecture of P. Erdös on the derivative of a polynomial;Lax, Peter D.;Bull. Amer. Math. Soc.,1944

5. Functions of exponential type;Rahman, Q. I.;Trans. Amer. Math. Soc.,1969

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