On the maximum modulus of polynomials not vanishing inside the unit circle
- Resource Type
- Article
- Authors
- Govil, N.
- Source
- Analysis in Theory and Applications; September 1989, Vol. 5 Issue: 3 p79-82, 4p
- Subject
- Language
- ISSN
- 16724070; 15738175
Abstract: A well-known theorem of Ankeney and Rivlin states that if p(z) is a polynomial of degree n, such that p(z)≠0 for |z|<1, then $$\mathop {max}\limits_{\left| z \right| - R \geqslant 1} \left| {p(z)} \right| \leqslant \left( {\frac{{R^n + 1}}{2}} \right)\mathop {max}\limits_{\left| z \right| = 1} \left| {p(z)} \right|$$ . In this paper we improve this bound.