# 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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