Anal. Theory Appl., 29 (2013), pp. 384-389.
Published online: 2013-11
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In this paper, we consider the class of polynomials $P(z)=a_{n}z^{n}+\sum_{\nu=\mu}^{n}a_{n-\nu}z^{n-\nu}$, $1\leq \mu\leq n$, having all zeros in $|z|\leq k$, $k\leq 1$ and thereby present an alternative proof, independent of Laguerre's theorem, of an inequality concerning the polar derivative of a polynomial.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2013.v29.n4.7}, url = {http://global-sci.org/intro/article_detail/ata/4532.html} }In this paper, we consider the class of polynomials $P(z)=a_{n}z^{n}+\sum_{\nu=\mu}^{n}a_{n-\nu}z^{n-\nu}$, $1\leq \mu\leq n$, having all zeros in $|z|\leq k$, $k\leq 1$ and thereby present an alternative proof, independent of Laguerre's theorem, of an inequality concerning the polar derivative of a polynomial.