@Article{ATA-34-175, author = {B. A. Zargar, A. W. Manzoor and Shaista Bashir}, title = {Inequalities Concerning the Maximum Modulus of Polynomials}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {2}, pages = {175--186}, abstract = {
Let $P(z)$ be a polynomial of degree $n$ having all its zeros in $|z|≤k$, $k≤1$, then
for every real or complex number $β$, with $|β|≤1$ and $R≥1$, it was shown by A. Zireh et
al. [7] that for $|z|=1$,
$$\min\limits_{|z|=1}\left|P(Rz)+\beta(\frac{R+k}{1+k})^nP(z)\right|\geq k^{-n}\left|R^n+\beta(\frac{R+k}{1+k})^n\right|\min\limits_{|z|=k}|P(z)|.$$
In this paper, we shall present a refinement of the above inequality. Besides, we shall
also generalize some well-known results.