Abstract
Sufficient conditions on
A
,
B
,
p
,
b
, and
c
are determined that will ensure the generalized Bessel function
u
p
,
b
,
c
satisfies the subordination
u
p
,
b
,
c
(
z
)
≺
1
+
A
z
/
(
1
+
B
z
)
. In particular this gives conditions for
(
-
4
κ
/
c
)
(
u
p
,
b
,
c
(
z
)
-
1
)
,
c
≠
0
, to be close-to-convex. Also, conditions for
u
p
,
b
,
c
(
z
)
to be Janowski convex and
z
u
p
,
b
,
c
(
z
)
to be Janowski starlike in the unit disk
D
=
z
∈
C
:
z
<
1
are obtained.