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Univalent α-Spiral Functions

Published online by Cambridge University Press:  20 November 2018

Richard J. Libera
Richard J. Libera*
Affiliation:
The University of Delaware, Newark, Delaware
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Suppose ƒ is regular in the open unit disk Δ, |z| < 1, and has a simple zero at the origin and no other zeros. Špaček (15) essentially showed that ƒ is univalent in Δ if and only if

such that 0 < r < 1 and 0 < t2 — t1 ⩽ 2π.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 449 - 456
Copyright
Copyright © Canadian Mathematical Society 1967

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