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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper Title:
Some Inequalities Concerning Derivative and Maximum Modulus of Polynomials
Author(s):
N. K. Govil, A. Liman and W. M. Shah
Department of Mathematics & Statistics,
Auburn University, Auburn,
Alabama 36849-5310,
U.S.A
Department of Mathematics,
National Institute of Technology,
Srinagar, Kashmir,
India - 190006
Department of Mathematics,
Kashmir University,
Srinagar, Kashmir,
India - 190006
govilnk@auburn.edu
abliman22@yahoo.com
wmshah@rediffmail.com
Abstract:
In this paper, we prove some compact generalizations of some well-known Bernstein type inequalities concerning the maximum modulus of a polynomial and its derivative in terms of maximum modulus of a polynomial on the unit circle. Besides, an inequality for self-inversive polynomials has also been obtained, which in particular gives some known inequalities for this class of polynomials. All the inequalities obtained are sharp.
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