#### Glasnik Matematicki, Vol. 37, No.1 (2002), 73-81.

### GROWTH OF MAXIMUM MODULUS OF POLYNOMIALS WITH
PRESCRIBED ZEROS

### Abdul Aziz and B. A. Zargar

P. G. Department of Mathematics, University of Kashmir, Srinagar
190006, India

**Abstract.** Let *P*(*z*) be a polynomial of
degree *n* not vanishing in |*z*| < *k* where
*k* ≥ 1. It is given
an upper bound for
max_{|z|=R>1}
|*P*(*z*)| in terms of *R,n,k*,
max_{|z|=1}
|*P*(*z*)| and
min_{|z|=k}
|*P*(*z*)|.
Among other things our result includes a refinement of a theorem due
to Ankeny and Rivilin as a special case. We shall also prove an
another result of similar nature.

**2000 Mathematics Subject Classification.**
30A06, 30A64.

**Key words and phrases.** Growth of Maximum Modulus,
inequalities for polynomials.

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