An inequality for derivatives of polynomials whose zeros are in a half-plane
Author:
Faruk F. Abi-Khuzam
Journal:
Proc. Amer. Math. Soc. 89 (1983), 119-124
MSC:
Primary 30C10; Secondary 30D20
DOI:
https://doi.org/10.1090/S0002-9939-1983-0706523-X
MathSciNet review:
706523
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a real polynomial of degree
all of whose zeros lie in the half-plane
. Let
be the maximum of
and
the counting function of the zeros of
. It is shown that the inequality
holds for
. It is also shown that Bernstein's inequality characterizes polynomials.
- [1] Abdul 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] J. E. Littlewood, Lectures on the theory of functions, Oxford Univ. Press, 1944. MR 0012121 (6:261f)
- [3] E. C. Titchmarsh, The theory of functions (2nd ed.), Oxford Univ. Press, 1939. MR 0197687 (33:5850)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1983-0706523-X
Article copyright:
© Copyright 1983
American Mathematical Society