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International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 233-238

Some inequalities for maximum modules of polynomials

Department of Algebra, Combinatorics & Analysis, Division of Mathematics, Auburn University, Auburn, AL, USA

Received 29 March 1990; Revised 20 August 1990

Copyright © 1991 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A well-known result of Ankeney and Rivlin states that if p(z) is a polynomial of degree n, such that p(z)0 in |z|<1, then max|z|=R1|p(z)|(Rn+12)max|z|=1|p(z)|. In this paper we prove some generalizations and refinements of this result.