Let
S
\mathcal {S}
be the usual class of univalent analytic functions on
|
z
|
>
1
\left | z \right | > 1
normalized by
f
(
0
)
=
0
f(0) = 0
and
f
′
(
0
)
=
1
f’(0) = 1
. Let
L
\mathfrak {L}
be the linear operator on
S
\mathcal {S}
given by
L
f
=
1
2
(
z
f
)
′
\mathfrak {L}f = \tfrac {1}{2}(zf)’
and let
r
S
t
{r_{{\mathcal {S}_t}}}
be the minimum radius of starlikeness of
L
f
\mathfrak {L}f
for
f
f
in
S
\mathcal {S}
. In 1947 R. M. Robinson initiated the study of properties of
L
\mathfrak {L}
acting on
S
\mathcal {S}
when he showed that
r
S
t
>
.38
{r_{{\mathcal {S}_t}}} > .38
. Later, in 1975, R. W. Barnard gave an example which showed
r
S
t
>
.445
{r_{{\mathcal {S}_t}}} > .445
. It is shown here, using a distortion theorem and Jenkin’s region of variability for
z
f
′
(
z
)
/
f
(
z
)
zf’(z)/f(z)
,
f
f
in
S
\mathcal {S}
, that
r
S
t
>
.435
{r_{{\mathcal {S}_t}}} > .435
. Also, a simple example, a close-to-convex half-line mapping, is given which again shows
r
S
t
>
.445
{r_{{\mathcal {S}_t}}} > .445
.