On a theorem of Duren, Shapiro and Shields
HTML articles powered by AMS MathViewer
- by Shinji Yamashita PDF
- Proc. Amer. Math. Soc. 73 (1979), 180-182 Request permission
Abstract:
We shall show that, an extension of the theorem of Duren, Shapiro and Shields on the univalence of a function f holomorphic in the unit disk D, still remains of significance, if the power $\alpha \in (0,1)$ in \[ {\sup _{z \in D}}{(1 - |z{|^2})^\alpha }|f''(z)/f’(z)|\] is small enough.References
- Jochen Becker, Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen, J. Reine Angew. Math. 255 (1972), 23–43 (German). MR 299780, DOI 10.1515/crll.1972.255.23
- Paul R. Beesack, Nonoscillation and disconjugacy in the complex domain, Trans. Amer. Math. Soc. 81 (1956), 211–242. MR 82009, DOI 10.1090/S0002-9947-1956-0082009-1
- P. L. Duren, H. S. Shapiro, and A. L. Shields, Singular measures and domains not of Smirnov type, Duke Math. J. 33 (1966), 247–254. MR 199359
- Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 180-182
- MSC: Primary 30C55
- DOI: https://doi.org/10.1090/S0002-9939-1979-0516460-0
- MathSciNet review: 516460