A refinement of an inequality due to Ankeny and Rivlin
DOI:
https://doi.org/10.24193/subbmath.2020.3.01Keywords:
Inequalities, polynomials, maximum modulus.Abstract
Let $p(z)= \sum_{\nu =0}^n a_\nu z^\nu$ be a polynomial of degree $n$, $ M(p,R):= \max_{|z|=R \ge 0} |p(z)|,$ and $M(p,1):=M(p)$. Then by well-known result due to Ankeny and Rivlin \cite{Ankeny}, we have M(p.R)≤(Rn+12)M(p), R≥1. In this paper, we sharpen and generalizes the above inequality by using a result due to Govil \cite{Govil1989}.
Mathematics Subject Classification (2010): 15A18, 30C10, 30C15, 30A10.
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