Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-12T21:51:16.370Z Has data issue: false hasContentIssue false
  • English
  • Français

On Odd Functions of Bounded Boundary Rotation

Published online by Cambridge University Press:  20 November 2018

Ronald J. Leach
Ronald J. Leach*
Affiliation:
Howard University, Washington, D.C.
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 VK denote the class of functions

that are analytic in the unit disc U, satisfy f′(z) ≠ 0 in U, and map U onto a domain with boundary rotation at most Kπ (for a definition of this concept, see [9]). V. Paatero [9] showed that f(z) ∊ VK if and only if

1.1

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 551 - 564
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Anderson, J. M., A note on starlike schlicht functions, J. London Math. Soc. 40 (1965), 713–718.Google Scholar
2. Brannan, D. A., On functions of bounded boundary rotation, I, Proc. Edinburgh Math. Soc. 16 (1969), 339–347.Google Scholar
3. Goluzin, G. M., Geometric theory of functions of a complex variable; Trans. Scripta Technica (American Mathematical Society, Providence, 1969).Google Scholar
4. Goluzin, G. M., On distortion theorems and coefficients of univalent functions, Mat. Sb. 19 (1946), 183–202.Google Scholar
5. Kaplan, W. K., Close-to-convex schlicht functions, Michigan Math. J. 1 (1952), 169–185.Google Scholar
6. Lehto, O., On the distortion of conformai mappings with bounded boundary rotation, Ann. Acad. Sci. Fenn. Ser. A I 124 (1952), 14 pp.Google Scholar
7. Lucas, K., On successive coefficients of areally mean p-vaient functions, J. London Math. Soc. 14 (1969), 631–642.Google Scholar
8. Noonan, J., Asympotic expressions for functions of bounded boundary rotation, Ph.D. Thesis, University of Maryland, 1970.Google Scholar
9. Paatero, V., Über die konforme Abbildungen von Gebieten deren Rander von beschrankter Drehung sind, Ann. Acad. Sci. Fenn. Ser. A I 33, 9 (1931), 77 pp.Google Scholar
10. Pommerenke, C., On the coefficients of close to convex functions, Michigan J. Math. 10 (1962), 259–269.Google Scholar
11. Pommerenke, C., On convex and starlike functions, J. London Math. Soc. 37 (1962), 209–224.Google Scholar
12. Riesz, F., Sur les fonctions subharmoniques et leur rapport a la théorie du potential, I, Acta. Math. 48 (1926), 329–343.Google Scholar
13. Robertson, M., Coefficients of functions with bounded boundary rotation, Can. J. Math. 21 (1969), 1477–1482.Google Scholar