Toshiyuki SUGAWA

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Inner radius of univalence for a strongly starlike domain
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Abstract

The inner radius of univalence of a domain `D` with Poincar'e density
`p`_{D} is the possible largest number `c` such that
the condition ||`S`_{f}||_{D}
=sup_{w}
`p`_{D}(`w`)^{-2}|`S`_{f}
(`z`)| < `c`
implies the univalence of `f` for a nonconstant meromorphic function
`f` on `D`, where `S`_{f}
is the Schwarzian drivative of `f`.
In this note, we will give a lower estimate of the inner radius
of univalence for strongly starlike domains of order `a`
with a concrete bound in terms of the order `a`.

submission: February 4, 2000

revision: February 8, 2000

revision: November 21, 2001

revision: November 22, 2001

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