Extension of Some Polynomial Inequalities to the Polar Derivative

M. S. Pukhta

Abstract


Let $p(z)$ be a polynomial of degree $n$ and ${D_\propto }p(z) = np(z) + (\propto - z)p'(z)$ denote the polar derivative of the polynomial $p(z)$ with respect to the point $\propto$. In this paper we obtain an inequality for the polar derivative of a polynomial which is an improvement of the result recently proved by Mir, Baba and Pukhta (2011) [Thai Journal of Mathematics, 9(2), 291--298].

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DOI: http://dx.doi.org/10.3968%2Fj.pam.1925252820120402.2135

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