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On Robinson's $ {1\over 2}$ conjecture


Author: Roger W. Barnard
Journal: Proc. Amer. Math. Soc. 72 (1978), 135-139
MSC: Primary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1978-0503547-0
MathSciNet review: 503547
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Abstract: In 1947, R. Robinson conjectured that if f is in S, i.e. a normalized univalent function on the unit disk, then the radius of univalence of $ [zf(z)]'/2$ is at least $ \tfrac{1}{2}$. He proved in that paper that it was at least .38. The conjecture has been shown to be true for most of the known subclasses of S. This author shows through use of the Grunski inequalities, that the minimum lower bound over the class S lies between .49 and .5.


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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0503547-0
Keywords: Univalent functions, Grunsky's inequalities
Article copyright: © Copyright 1978 American Mathematical Society

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