#### Glasnik Matematicki, Vol. 32, No.1 (1997), 45-51.

### GENERALIZATION OF CERTAIN WELL KNOWN
INEQUALITIES FOR POLYNOMIALS

### V. K. Jain

Mathematics Department, I.I.T., Kharagpur - 721302, India

**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*)
(*R*^{n}+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.

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