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Polynomials with a Prescribed Zero and the Bernstein's Inequality
Published online by Cambridge University Press: 20 November 2018
Abstract
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Let be the class of all polynomials/? of degree at most n such that In view of the example zn it follows from Bernstein's inequality for polynomials that at each point z0 of the unitcirle. It was shown by A. Giroux and Q. I. Rahman [2] that if denotes the subclass of polynomials in which vanish at 1, then
where c1 and c2 are constants not depending on n. Here we find the exact value of which has some special significance and also at certain other points of the unit circle.
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- Copyright © Canadian Mathematical Society 1993
References
1.
Frappier, C., Rahman, Q. I. and St. Ruscheweyh, On polynomials with a prescribed zero, Constr. Approx. 2(1986), 171–177.Google Scholar
2.
Giroux, A. and Rahman, Q. I., Inequalities for polynomials with a pre scribed zero, Trans. Amer. Math. Soc. 193(1974), 67–98.Google Scholar
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