Author:
Hu Zhenyong,Fan Jinhua,Wang Xiaoyuan
Abstract
UDC 517.5
Suppose that
p
(
z
)
=
1
+
z
ϕ
'
'
(
z
)
/
ϕ
'
(
z
)
,
where
ϕ
(
z
)
is a locally univalent analytic function in the unit disk
D
with
ϕ
(
0
)
=
ϕ
'
(
1
)
-
1
=
0.
We establish the lower and upper bounds for the best constants
σ
0
and
σ
1
such that
e
-
σ
0
/
2
<
|
p
(
z
)
|
<
e
σ
0
/
2
and
|
p
(
w
)
/
p
(
z
)
|
<
e
σ
1
for
z
,
w
∈
D
,
respectively, imply the univalence of
ϕ
(
z
)
in
D
.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science