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Journal of the Ramanujan Mathematical Society

Volume 29, Issue 4, December 2014  pp. 403–412.

On the polar derivative of a polynomial

Authors:  Abdullah Mir and Bilal Dar
Author institution:Department of Mathematics, University of Kashmir, Srinagar 190 006, India

Summary:  Let P(z) be a polynomial of degree $n$ and for any complex number Α, let D Α P(z) = nP(z) + (Α - z)P'(z) denote the polar derivative of the polynomial P(z) with respect to Α. In~this paper, we obtain certain inequalities for the polar derivative of a polynomial with restricted zeros. Our results generalize and sharpen some well-known polynomial inequalities.

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