On the radius of starlikeness of for univalent

Author:
Roger W. Barnard

Journal:
Proc. Amer. Math. Soc. **53** (1975), 385-390

MSC:
Primary 30A32

DOI:
https://doi.org/10.1090/S0002-9939-1975-0382615-8

MathSciNet review:
0382615

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the standard class of normalized univalent functions. For a given function , regular for , let be the radius of starlikeness of . In 1947, R. M. Robinson considered the combination for . He found a lower bound of .38 for for all . He noted that the standard Koebe function , has its equal to . A question that has been asked since Robinson's paper is whether is the minimum for all in . It is shown here that this is not the case by giving examples of functions whose is less than .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0382615-8

Keywords:
Univalent functions,
starlike function,
radius of starlikeness

Article copyright:
© Copyright 1975
American Mathematical Society