Year: 2018
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2018.v34.n2.7
Analysis in Theory and Applications, Vol. 34 (2018), Iss. 2 : pp. 175–186
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Growth of polynomials minimum modulus of polynomials inequalities.