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On Regions Omitted By Univalent Functions II

Published online by Cambridge University Press:  20 November 2018

A. W. Goodman  and
E. Reich
A. W. Goodman
Affiliation:
University of Kentucky
E. Reich
Affiliation:
Institute for Advanced Study
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1. Introduction. Let S denote the family of functions f(z) regular and univalent in ∣z∣ < 1, with the expansion f(z) = z + a2z2 + … about z = 0, and let Af denote the area of the intersection of the open circle ∣ω∣ < 1 with Df, the image of ∣z∣ < 1 under f(z). A few years ago one of the authors (1) proved that if

1

then

2.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 83 - 88
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Goodman, A. W., Note on regions omitted by univalent functions, Bull. Amer. Math. Soc, 55 (1949), 363–369.Google Scholar
2. Jenkins, J. A., On values omitted by univalent functions, Amer. J. Math., 75 (1953), 406–408.Google Scholar