The classes
K
n
{K_n}
of functions
f
(
z
)
f(z)
regular in the unit disc
U
\mathfrak {U}
with
f
(
0
)
=
0
,
f
′
(
0
)
=
1
f(0) = 0,f’(0) = 1
satisfying
\[
Re
[
(
z
n
f
)
(
n
+
1
)
/
(
z
n
−
1
f
)
(
n
)
]
>
(
n
+
1
)
/
2
\operatorname {Re} [{({z^n}f)^{(n + 1)}}/{({z^{n - 1}}f)^{(n)}}] > (n + 1)/2
\]
in
U
\mathfrak {U}
are considered and
K
n
+
1
⊂
K
n
,
n
=
0
,
1
,
⋯
{K_{n + 1}} \subset {K_n},n = 0,1, \cdots
, is proved. Since
K
0
{K_0}
is the class of functions starlike of order 1/2 all functions in
K
n
{K_n}
are univalent. Some coefficient estimates are given and special elements of
K
n
{K_n}
are determined.