On an inequality concerning the polar derivative of a polynomial with restricted zeros

N. A. Rather; Suhail Gulzar

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arXiv · 1404.6600

On an inequality concerning the polar derivative of a polynomial with restricted zeros

N. A. Rather·Suhail Gulzar

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Abstract

Let $D_αP(z)=nP(z)+(α-z)P^{\prime}(z)$ denote the polar derivative of a polynomial $P(z)$ of degree $n$ with respect to a point $α\in\mathbb{C}.$ In this paper, we present a correct proof, independent of Laguerre's theorem, of an inequality concerning the polar derivative of a polynomial with restricted zeros recently formulated by K. K. Dewan, Naresh Singh, Abdullah Mir, [Extensions of some polynomial inequalities to the polar derivative, \emph{J. Math. Anal. Appl.,} \textbf{352} (2009) 807-815].

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N. A. Rather, Suhail Gulzar. 2014-04-26. On an inequality concerning the polar derivative of a polynomial with restricted zeros. https://arxiv.org/abs/1404.6600

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