• Inequalities for a polynomial and its derivative

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/110/02/0137-0146

• # Keywords

Inequalities; zeros; polynomial

• # Abstract

For an arbitrary entire functionf and anyr&gt;0, letM(f,r):=max|z|=r |f(z)|. It is known that ifp is a polynomial of degreen having no zeros in the open unit disc, andm:=min|z|=1|p(z)|, then$$\begin{gathered} M(p',1) \leqslant \frac{n}{2}\{ M(p,1) - m), \hfill \\ M(p,R) \leqslant \left( {\frac{{R^n + 1}}{2}} \right)M(p,1) - m\left( {\frac{{R^n - 1}}{2}} \right),R &gt; 1 \hfill \\ \end{gathered}$$ It is also known that ifp has all its zeros in the closed unit disc, then$$M(p',1) \geqslant \frac{n}{2}\{ M(p,1) - m\}$$. The present paper contains certain generalizations of these inequalities.

• # Author Affiliations

1. Mathematics Department, Indian Institute of Technology, Kharagpur - 721 302, India

• # Proceedings – Mathematical Sciences

Volume 132, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019

Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.