Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-12-03T20:41:55.064Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on a Class of Slit Conformal Mappings

Published online by Cambridge University Press:  20 November 2018

W. E. Kirwan  and
R. W. Pell
W. E. Kirwan
Affiliation:
University of Maryland, College Park, Maryland
R. W. Pell
Affiliation:
University of Maryland, College Park, Maryland
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.

We denote by 5 the class of functions, f(z), that are analytic and univalent in U = ﹛z: |z| < 1﹜ and have the normalization

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1166 - 1173
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Aksent'ev, L. A., Application of the argument principle to the study of schlichtness conditions II, Izv. Vyss. Ucebn. Zaved, Matematika No. 12 (1969), 3.15.Google Scholar
2. Avkhacliev, F. G. and Aksent'ev, L. A., The main results on sufficient conditions for an analytic function to be schlicht, Russian Math. Surveys 30:4 (1975), 1–64.Google Scholar
3. Brickman, L., Extreme points of the set of univalent functions, Bull. Amer. Math. Soc. 70 (1970), 372–374.Google Scholar
4. Brickman, L. and Wilken, D., Support points of the set of univalent functions, Proc. Amer. Math. Soc. 42 (1974), 523–528.Google Scholar
5. Brickman, L. and Wilken, D., XV. Hengartner and Schober, G., Extreme points for univalent functions, Trans. Amer. Math. Soc. 185 (1973), 265–270.Google Scholar
6. Brickman, L. and Wilken, D., XV. Hengartner and Schober, G., Some new properties of support points for compact families of univalent functions in the unit disc, Mich. Math. J. 23 (1976), 207–216.Google Scholar
7. Lowner, K., Untersuchungen iiber schlicte konforme abbildungen des Einheitskresses, Math. Ann. 89, 102–121.Google Scholar
8. Markushevich, A. I., Theory of functions of a complex variable, Vol. II (Prentice Hall, Englewood Cliffs, New Jersey, 1965).Google Scholar
9. Pfluger, A., Linear Extremal problems bei schlichten Functionen, Ann. Acad. Sci. Fenn. Ser. AI 489 (1971).Google Scholar
10. Pommerenke, Chr., Uber die Subordination analytischer Functionen, J. Reine Angew. Math. 218 (1965), 159–173.Google Scholar
11. Pommerenke, Chr. Univalent functions (Vandenhoech and Ruprecht, Gôttingen, 1973).Google Scholar