TY - JOUR
T1 - Inequalities Concerning the Maximum Modulus of Polynomials
JO - Analysis in Theory and Applications
VL - 2
SP - 175
EP - 186
PY - 2018
DA - 2018/07
SN - 34
DO - http://doi.org/10.4208/ata.2018.v34.n2.7
UR - https://global-sci.org/intro/article_detail/ata/12585.html
KW - Growth of polynomials, minimum modulus of polynomials, inequalities.
AB - <p style="text-align: justify;">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 $|z|=1$,<br/>$$\min\limits_{|z|=1}\left|P(Rz)+\beta(\frac{R+k}{1+k})^nP(z)\right|\geq k^{-n}\left|R^n+\beta(\frac{R+k}{1+k})^n\right|\min\limits_{|z|=k}|P(z)|.$$<br/>In this paper, we shall present a refinement of the above inequality. Besides, we shall
also generalize some well-known results.</p>