INEQUALITIES FOR A POLYNOMIAL AND ITS DERIVATIVE .2.

A well-known result of Rivlin states that if p(z) is a polynomial of degree n, such that p(z) not equal 0 in \z\ < 1, then max(\z\=r<1) \p(z)\ greater than or equal to ((r + 1)/2)(n) max(\z\=1), \p(z)\. In this paper, we consider the polynomial p(z) = a(0) + Sigma(v=mu)(n) a(v)z(v) having all its zeros in \z\ greater than or equal to k > 1 and obtain a generalization of this result, Our result improves upon a result recently proved by Bidkham and Dewan (J. Math. Anal. Appl. 166 (1992),319-324). (C) 1995 Academic Press, Inc.