Glasnik matematički, Vol. 33 No. 1, 1998.
Original scientific paper
Certain interesting implications of T. J. Rivlin's result on maximum modulus of a polynomial
V. K. Jain
Abstract
Let f(z) be an arbitrary entire function and M(f,r) = max|z|=r |f(z)|. For a polynomial p(z) of degree n, having no zeros in |z| < 1, Rivlin had obtained
M(p,r) ≥ ((r+1)/2)n M(p,1), r ≤ 1.
Using this and various associated results, we have obtained precise relationship between M(p,ρ), and M(p,1) for polynomials p(z) having all its zeros on |z| = k, k > 0. Some sort of a converse of Rivlin's result has also been obtained.
Keywords
Hrčak ID:
8169
URI
Publication date:
1.6.1998.
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