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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Asymptotic Inequalities for the Maximum Modulus of the Derivative of a Polynomial
Author(s):
Clément Frappier
Département de Mathématiques et de Génie industriel École Polytechnique de
Montréal,
C.P.~6079, succ. Centre-ville Montréal (Québec),
H3C 3A7, CANADA
Abstract:
Let
be an algebraic polynomial of degree
≤n, and let ∥p∥= max {|p(z)|:|z| = 1}.
We study the asymptotic behavior of the best possible constant φn,k (R), for
k = 0 and k=1, in the inequality ∥p'(Rz)∥ + φn,k (R) |ak|
≤ nRn-1 ∥p∥, R → ∞.
Paper's Title:
An Lp Inequality for `Self-Reciprocal' Polynomials. II
Author(s):
M. A. Qazi
Department of Mathematics,
Tuskegee University,
Tuskegee, Alabama 36088
U.S.A.
Abstract:
The main result of this paper is a sharp integral mean inequality for the derivative of a `self-reciprocal' polynomial.
Paper's 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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