Let p(z) be a polynomial of degree n and for any real or 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 inequalities for the polar derivative of a polynomial having all its zeros inside or outside a circle. Our results shall generalize and sharpen some well-known polynomial inequalities.

This paper deals with the problem of finding some upper bound estimates for the maximum modulus of a univariate complex polynomial on a disk under certain constraints on the zeros and on the functions involved. A variety of interesting results follow as special cases from our general results.

In this paper, we obtain a result that improves the results of Govil and Nwaeze, Qazi and the classical result of Rivlin.

Let f(z) be an arbitrary entire function and M(f,r)=max|z|=r|f(z)|. For a polynomial P(z), having no zeros in |z|

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