Rate of Growth of Polynomials Not Vanishing Inside a Circle
A well known result due to Ankeny and Rivlin  states that if p(z) = ∑v=0n avzv is a polynomial of degree n satisfying p(z) ≠ 0 for |z| < 1 then for R > 1 max |z|=R|p(Z)| ≤Rn+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 + ∑v=tn a vzv1 ≤ t ≤ n which have no zeros in |z| < K, K ≥1.
Gardner, Robert B.; Govil, N. K.; and Musukula, Srinath R.. 2005. Rate of Growth of Polynomials Not Vanishing Inside a Circle. Journal of Inequalities in Pure and Applied Mathematics. Vol.6(2). ISSN: 1443-5756