Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-09T00:28:05.420Z Has data issue: false hasContentIssue false
  • English
  • Français

On univalent polynomials

Published online by Cambridge University Press:  18 May 2009

David A. Brannan
David A. Brannan
Affiliation:
University of Glasgow, Glasgow, W.2
Rights & Permissions [Opens in a new window]

Extract

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 Pn be the class of normalised polynomials of the form

of degree n which are univalent in U = {|z| < 1}. In this note we discuss the coefficients of polynomials in Pn and in some of its subclasses.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 11 , Issue 2 , July 1970 , pp. 102 - 107
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

REFERENCES

1.Alexander, J. W., Functions which map the interior of the unit circle upon simple regions, Annals of Math. 17 (1915), 12–22.CrossRefGoogle Scholar
2.Brannan, D. A., On univalent polynomials and related classes of functions, Thesis, University of London (1967).Google Scholar
3.Brannan, D. A., Coefficient regions for univalent polynomials of small degree, Mathematika 14 (1967), 165–169.CrossRefGoogle Scholar
4.Brannan, D. A. and Brickman, L., Coefficient regions for starlike polynomials; to appear.Google Scholar
5.Cowling, V. F. and Royster, W. C., Domains of variability for univalent polynomials, Proc. Amer. Math. Soc. 19 (1968), 767–772.CrossRefGoogle Scholar
6.Dieudonné, J., Sur le rayon d'univalence des polynomes, C. R. Acad. Sci. Paris 192 (1931), 78–81.Google Scholar
7.Hayman, W. K., Multivalent functions, Cambridge University Press (1958).Google Scholar
8.Kaplan, W., Close-to-convex schlicht functions, Michigan Math. J. 1 (1952), 169–185.CrossRefGoogle Scholar
9.Marden, M., The geometry ofthe zeros ofa polynomial in a complex variable, New York (1949).Google Scholar
10.Suffridge, T. J., On univalent polynomials, J. London Math. Soc. (2) 44 (1969), 496–504.CrossRefGoogle Scholar