Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Tangential limits of starlike univalent functions


Author: J. B. Twomey
Journal: Proc. Amer. Math. Soc. 97 (1986), 49-54
MSC: Primary 30C45; Secondary 30D40
MathSciNet review: 831385
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f$ be starlike univalent in the unit disc, let $ \gamma > 1$ and let $ K > 0$. Then $ f(z)$ tends to a limit as $ z \to {e^{i\theta }}$ inside $ \{ z:\left\vert {{e^{i\theta }} - z} \right\vert \leq K{(1 - \left\vert z \right\vert)^{1/\gamma }}\} $ for every $ \theta $ in $ [0,2\pi ]$. This result is sharp.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C45, 30D40

Retrieve articles in all journals with MSC: 30C45, 30D40


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0831385-2
PII: S 0002-9939(1986)0831385-2
Keywords: Tangential limits, univalent functions, starlike functions
Article copyright: © Copyright 1986 American Mathematical Society