International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2641-2645

On the maximum modulus of a polynomial and its derivatives

K. K. Dewan and Abdullah Mir

Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia (Central University), New Delhi 110025, India

Received 18 February 2005; Revised 5 April 2005

Copyright © 2005 K. K. Dewan and Abdullah Mir. 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.


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|<k, k1, Bidkham and Dewan (1992) proved max|z|=r|P(z)|(n(r+k)n1/(1+k)n)max|z|=1|P(z)| for 1rk. In this paper, we generalize as well as improve upon the above inequality.