Anal. Theory Appl., 30 (2014), pp. 290-295.
Published online: 2014-10
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In this paper we consider a class of polynomials $P(z)= a_{0} + \sum_{v=t}^{n} a_{v}z^{v}$, $t\geq 1,$ not vanishing in $|z|<k,$ $ k\geq 1$ and investigate the dependence of ${\max_{|z|=1}}|P(Rz)-P(rz)|$ on ${\max_{|z|=1}}|P(z)|,$ where $ 1 \leq r < R.$ Our result generalizes and refines some known polynomial inequalities.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n3.5}, url = {http://global-sci.org/intro/article_detail/ata/4493.html} }In this paper we consider a class of polynomials $P(z)= a_{0} + \sum_{v=t}^{n} a_{v}z^{v}$, $t\geq 1,$ not vanishing in $|z|<k,$ $ k\geq 1$ and investigate the dependence of ${\max_{|z|=1}}|P(Rz)-P(rz)|$ on ${\max_{|z|=1}}|P(z)|,$ where $ 1 \leq r < R.$ Our result generalizes and refines some known polynomial inequalities.