Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-17T18:07:24.792Z Has data issue: false hasContentIssue false

Polynomials with a Prescribed Zero and the Bernstein's Inequality

Published online by Cambridge University Press:  20 November 2018

P. F. Olivier
Affiliation:
Dalhousie University, Department of Mathematics, Halifax, Nova Scotia, B3H3J5, email:, [email protected]
A. O. Watt
Affiliation:
Ecole Polytechnique de Thies, B.P. 10 Thies Senegal
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Copyright
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), 171177.Google Scholar
2. Giroux, A. and Rahman, Q. I., Inequalities for polynomials with a pre scribed zero, Trans. Amer. Math. Soc. 193(1974), 6798.Google Scholar