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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