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Let f (z) be an arbitrary entire function and M(f ,r) = max |z|=r | f (z)|. For a polynomial P(z) of degree n, having no zeros in |z| < k, k ≥ 1, Bidkham and Dewan (1992) proved max |z|=r |P (z)| ≤ (n(r + k) n−1 /(1 + k) n)max |z|=1 |P(z)| for 1 ≤ r ≤ k. In this paper, we generalize as well as improve upon the above inequality.

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