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  • 1 Auburn University Department of Mathematics Auburn Al 36849-5310 U.S.A Auburn Al 36849-5310 U.S.A
  • | 2 Ferris State University Department of Mathematics Big Rapids Mi 49307-2225 U.S.A Big Rapids Mi 49307-2225 U.S.A
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Abstract  

Let p(z) be a polynomial of degree n and for a complex number α, let Dαp(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 inequalities for the polar derivative of a polynomial having all its zeros in |z| ≤ K. Our results generalize and sharpen a famous inequality of Turn and some other known results in this direction.

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