Abstract. Let p(z) be a polynomial of degree n and M(f,r) = max|z|=r |f(z)|, for an arbitrary entire function f(z). For p(z) not vanishing in |z| < 1, we have M(p',1) n/2 M(p,1) and M(p,R) (Rn+1)/2 M(p,1), R > 1. Certain generalizations of these inequalities have been obtained. The inequalities are sharp. Some applications are also considered.
1991 Mathematics Subject Classification. 30C10, 30A10.
Key words and phrases. Inequalities, generalization.