A new proof and a generalization of a theorem of de Bruijn
Author:
Abdul Aziz
Journal:
Proc. Amer. Math. Soc. 106 (1989), 345350
MSC:
Primary 30A10; Secondary 26C05, 30C10
MathSciNet review:
933511
Fulltext PDF Free Access
Abstract 
References 
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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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Abdul
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 [1]
 A. Aziz and Q. G. Mohammad, Simple proof of a theorem of Erdös and Lax, Proc. Amer. Math. Soc. 80 (1980), 119122. MR 574519 (81g:30008)
 [2]
 N. G. De Bruijn, Inequalities concerning polynomials in the complex domain, Nederl. Akad. Wetensch. Proc. 50 (1947), 12651272 = Indag. Math. 9 (1947), 591598. MR 0023380 (9:347e)
 [3]
 K. K. Dewan and N. K. Govil, An inequality for selfinversive polynomials, J. Math. Anal. Appl. 95 (1983), 490. MR 716098 (84i:30001)
 [4]
 P. D. Lax, Proof of a conjecture of P. Erdös on the derivative of a polynomial, Bull. Amer. Math. Soc. 50 (1944), 509513. MR 0010731 (6:61f)
 [5]
 Q. I. Rahman, Functions of exponential type, Trans. Amer. Math. Soc. 135 (1969), 295309. MR 0232938 (38:1261)
 [6]
 A. C. Schaeffer, Inequalities of A. Markoff and S. Bernstein for polynomials and related functions, Bull. Amer. Math. Soc. 47 (1941), 565579. MR 0005163 (3:111a)
 [7]
 A. Zygmund, A remark on conjugate series, Proc. London Math. Soc. (2) 34 (1932), 392400.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198909335116
PII:
S 00029939(1989)09335116
Keywords:
Derivative of a polynomial,
integral mean estimates,
inequalities in the complex domain,
selfinversive polynomials
Article copyright:
© Copyright 1989
American Mathematical Society
