On Robinson's 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 is at least . 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.

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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