Rate of Growth of Polynomials Not Vanishing inside a Circle
نویسندگان
چکیده
A well known result due to Ankeny and Rivlin [1] states that if p(z) = ∑n v=0 avz v is a polynomial of degree n satisfying p(z) 6= 0 for |z| < 1 then for R ≥ 1 max |z|=R |p(z)| ≤ R n + 1 2 max |z|=1 |p(z)|. It was proposed by late Professor R.P. Boas, Jr. to obtain an inequality analogous to this inequality for polynomials having no zeros in |z| < K, K > 0. In this paper, we obtain some results in this direction, by considering polynomials of the form p(z) = a0 + ∑n v=t avz , 1 ≤ t ≤ n which have no zeros in |z| < K, K ≥ 1.
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