On maximum modulus for the derivative of a polynomial

Abstract

If P(z) is a polynomial of degree n, having all its zeros in the diskjzj k, k 1, then it was shown by Govil (Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546) that maxzj=1 P 0 (z) n 1 +kn max jzj=1 jP(z)j: In this paper, we obtain generalization as well as improvement of above in- equality for the polynomial of the type P(z) = c0 + P n = c z , 1 n. Also we generalize a result due to Dewan and Mir (Southeast Asian Bull. Math. 31 (2007), 691-695) in this direction.