AN Lp INEQUALITY FOR
POLYNOMIALS NOT VANISHING IN A DISK
R.N. Ahmed1, Suhail Gulzar2
Department of Mathematics
University of Kashmir
Harzarbal, Sringar, 190 006, INDIA
Abstract. For the class of polynomials P(z)=a0+∑ν=μnaνzν, 1 ≤ μ ≤ n, of degree n not vanishing in the disk |z| < k where k ≥ 1, we investigate the dependence of ||P(Rz)-P(rz)||p on ||P(z)||p for R>r≥1, p>0 and present compact generalizations of certain well-known polynomial inequalities.
Received: March 29, 2013
AMS Subject Classification: 30C10, 30A10, 41A17


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DOI: 10.12732/ijam.v26i2.8

Volume: 26
Issue: 2
Year: 2013