Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

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.

References [Enhancements On Off] (What's this?)

  • [1] A. Aziz and Q. G. Mohammad, Simple proof of a theorem of Erdös and Lax, Proc. Amer. Math. Soc. 80 (1980), 119-122. MR 574519 (81g:30008)
  • [2] N. G. De Bruijn, Inequalities concerning polynomials in the complex domain, Nederl. Akad. Wetensch. Proc. 50 (1947), 1265-1272 = Indag. Math. 9 (1947), 591-598. MR 0023380 (9:347e)
  • [3] K. K. Dewan and N. K. Govil, An inequality for self-inversive 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), 509-513. MR 0010731 (6:61f)
  • [5] Q. I. Rahman, Functions of exponential type, Trans. Amer. Math. Soc. 135 (1969), 295-309. 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), 565-579. MR 0005163 (3:111a)
  • [7] A. Zygmund, A remark on conjugate series, Proc. London Math. Soc. (2) 34 (1932), 392-400.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30A10, 26C05, 30C10

Retrieve articles in all journals with MSC: 30A10, 26C05, 30C10

Additional Information

Keywords: Derivative of a polynomial, integral mean estimates, inequalities in the complex domain, self-inversive polynomials
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society