On the radius of convexity and boundary distortion of Schlicht functions
Author:
David E. Tepper
Journal:
Trans. Amer. Math. Soc. 150 (1970), 519-528
MSC:
Primary 30.42
DOI:
https://doi.org/10.1090/S0002-9947-1970-0268370-0
MathSciNet review:
0268370
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be regular and univalent for
and map
onto a region which is starlike with respect to
. If
denotes the radius of convexity of
,
for
, and
for
, then it has been conjectured that
. It is shown here that
, which improves the old estimate
. In addition, sharp estimates for
are given which depend on the value of
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1970-0268370-0
Keywords:
Schlicht functions,
convex and starlike functions,
radius of convexity
Article copyright:
© Copyright 1970
American Mathematical Society