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Coefficients of Functions with Bounded Boundary Rotation

Published online by Cambridge University Press:  20 November 2018

M. S. Robertson
M. S. Robertson*
Affiliation:
University of Delaware, Newark, Delaware
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For fixed k ≧ 2, let Vk denote the class of normalized analytic functions

such that z ∈ E = {z; |z| <1} are regular and have f′(0) = l,f′(z) ≠ 0, and

1

Let Sk be the subclass of Vk whose members f(z) are univalent in E. It was pointed out by Paatero (4) that Vk coincides with Sk whenever 2 ≦ k ≦ 4. Later Rényi (5) showed that in this case, f(z) ∈ Sk is also convex in one direction in E. In (6) I showed that the Bieberbach conjecture

holds for functions convex in one direction.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 1477 - 1482
Copyright
Copyright © Canadian Mathematical Society 1969

References

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