@Article{ATA-33-219,
author = {N. K. Govil and E. R. Nwaeze},
title = {Some Sharpening and Generalizations of a Result of T. J. Rivlin},
journal = {Analysis in Theory and Applications},
year = {2017},
volume = {33},
number = {3},
pages = {219--228},
abstract = {<p style="text-align: justify;">Let $p(z)=a_0+a_1z+a_2z^2+a_3z^3+\cdots+a_nz^n$ be a polynomial of degree $n$. Rivlin [12] proved that if $p(z)\neq 0$ in the unit disk, then for $0&lt; r\leq 1,$ $${\max_{|z|=r}|p(z)|}\geq \Big(\dfrac{r+1}{2}\Big)^n{\max_{|z|=1}|p(z)|}.$$ In this paper, we prove a sharpening and generalization of this result and show by means of examples that for some polynomials our result can significantly improve the bound obtained by the Rivlin&#39;s Theorem.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2017.v33.n3.3},
url = {http://global-sci.org/intro/article_detail/ata/10513.html}
}