Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T02:36:27.217Z Has data issue: false hasContentIssue false
  • English
  • Français

Curvature and Radius of Curvature for Functions with Bounded Boundary Rotation

Published online by Cambridge University Press:  20 November 2018

J. W. Noonan
J. W. Noonan*
Affiliation:
College of the Holy Cross, Worcester, Massachusetts
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.

For k ≧ 2 denote by Vk the class of functions f regular in and having the representation

(1.1)

where μ is a real-valued function of bounded variation on [0, 2π] with

(1.2)

Vk is the class of functions with boundary rotation at most kπ.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 1015 - 1023
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Goluzin, G. M., Geometric theory of functions of a complex variable, Translations of Mathematical Monographs, Vol. 26 (Amer. Math. Soc, Providence, Rhode Island, 1969).Google Scholar
2. Hille, E., Analytic function theory, Vol. II (Blaisdell, New York, 1962).Google Scholar
3. Keogh, F. R., Some inequalities for convex and star-shaped domains, J. London Math. Soc. 29 (1954), 121–123.Google Scholar
4. Lehto, O., On the distortion of conformal mappings with bounded boundary rotation, Ann. Acad. Sci. Fenn. Ser. Al 124 (1952), 14p.Google Scholar
5. Robertson, M. S., Coefficients of functions with bounded boundary rotation, Can. J. Math. 21 (1969), 1477–1482.Google Scholar
6. Zmorovič, V. A., On certain variational problems of the theory of univalent functions, Ukrain. Mat. Z. 4 (1952), 276–298.Google Scholar