Univalent α-Spiral Functions
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 449-456

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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.
Libera, Richard J. Univalent α-Spiral Functions. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 449-456. doi: 10.4153/CJM-1967-038-0
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