Abstract
A normalized univalent function
f is called Ma–Minda starlike or convex if
zf
′
(
z
)
/
f
(
z
)
≺
φ
(
z
)
or
1
+
zf
″
(
z
)
/
f
′
(
z
)
≺
φ
(
z
)
where
φ
is a convex univalent function with
φ
(
0
)
=
1
. The class of Ma–Minda convex functions is shown to be closed under certain operators that are generalizations of previously studied operators. Analogous inclusion results are also obtained for subclasses of starlike and close-to-convex functions. Connections with various earlier works are made.