IJPAM: Volume 89, No. 1 (2013)

INTEGRAL MEAN ESTIMATES FOR POLYNOMIALS
WITH RESTRICTED ZEROS

N.A. Rather$^1$, Suhail Gulzar$^2$
$^{1,2}$Department of mathematics
University of Kashmir
Harzarbal, Sringar 190006, INDIA


Abstract. Let $P(z)$ be a polynomial of degree $n$ having all its zeros in $\vert z\vert\leq k$, where $k\leq 1,$ then for each $r>0,$ $p>1,q>1$ with $p^{-1}+q^{-1}=1,$ it was proved by Aziz and Ahemad [#!ar96!#]: \begin{equation*} n\Bigg\{\int\limits_{0}^{2\pi}\left\vert P\left(e^{i\theta}\r... ...P^{\prime}(e^{i\theta})\vert^{pr}d\theta\Bigg\}^{\frac{1}{pr}}. \end{equation*} In this paper, we establish some refinements and generalizations of above and some known polynomial inequalities concerning the polar derivative of a polynomial with restricted zeros.

Received: March 29, 2013

AMS Subject Classification: 30C10, 30A10, 41A17

Key Words and Phrases: polynomials, inequalities in the complex domain, polar derivative

Download paper from here.


DOI: 10.12732/ijpam.v89i1.2 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 1