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Let P(z) be a polynomial of degree n having no zeros in |z| < k where k ≥ 1. Then it is known that for every real or complex number α with |α| ≥ 1, max |z|=1 |DαP(z)| ≤ n (|α| + k/1 + k) max |z|=1 |P(z)|, where DαP(z) = nP(z) + (α - z)P' (z) denotes the polar derivative of the polynomial P(z) of degree n with respect to a point α ∈ ℂ. In this paper, by a simple method, a refinement of the above inequality and other related results are obtained. [ABSTRACT FROM AUTHOR]

In this paper we obtain some refinements of a well-known result of Enestr om- Kakeya concerning the bounds for the moduli of the zeros of polynomials with complex coefficients which improve upon some results due to Aziz and Mohammad, Govil and Rahman and others. [ABSTRACT FROM AUTHOR]