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) <= (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.


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