Abstract. If P (z) is a polynomial of degree n, having all its zeros in the disk |z| ≤ k, k ≥ 1, then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] thatIn this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type P (z) = c0 + n ν=µ cν z ν , 1 ≤ µ ≤ n. Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.

Let p(z) be a polynomial of degree n , having no zeros in |z| < k , k ≥ 1 , then Aziz [In this paper we first generalize as well as improves upon the above inequality which in turns also gives generalization and improvement of some well known inequalities. Besides,we also generalize as well as improves upon a result due to Govil [ J. Approx. Theory, Vol. 66 (1991), pp. 29-35] by extending it to Polar derivative.

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.

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