IJPAM: Volume 34, No. 1 (2007)

INTEGRAL INEQUALITIES FOR POLYNOMIALS

N.A. Rather$^1$, M.I. Mir$^2$
$^{1,2}$Department of Mathematics
University of Kashmir
Hazratbal, Srinagar, 190006, INDIA
$^1$e-mail: nisararather@yahoo.co.in
$^2$e-mail: mohdibrahimrakh@yahoo.com


Abstract.Let $P(z)$ be a polynomial of degree $n$ which does not vanish in $\vert z\vert<k$. For $k=1$, it is known that

\begin{displaymath} \vert\vert P(Rz)\vert\vert _r\le \frac{\vert\vert 1+R^n z^n... ...t _r}\vert\vert P(z)\vert\vert _r,\qquad0<r<\infty,\qquad R>1. \end{displaymath}

In this paper we consider the case $k\ge 1$ and obtain a more general result which yields variety of interesting generalizations of some known polynomial inequalities.

Received: October 17, 2006

AMS Subject Classification: 26D10, 41A17

Key Words and Phrases: $L_p$-inequalities, polynomials

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 1