In this paper, we study the growth of polynomials of degree n having all its zeros on |z| = k , k 1. Using the notation M(p,t) = max |z|=t |p(z)| , we measure the growth of p by estimating M(p,t) M(p,1

Abstract. In this paper we obtain certain results for the polar derivative of a polynomial p(z) = cnz n + n j=µ cn−jz n−j , 1 ≤ µ ≤ n, having all its zeros on |z| = k, k ≤ 1, which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.

If p(z) is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then itIn this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type p(z) = c n z n + n ∑ j=μ c n− j z n− j , 1 ≤ μ ≤ n. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.

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