Abstract
Let
A
denote the class of analytic functions
f
, in the open unit disk
E
= {
z
: |
z
| < 1}, normalized by
f
(0) =
f
′(0) − 1 = 0. In this paper, we introduce and study the class
of functions
, with
, satisfying
where
is a convex function in
E
with
h
(0) = 1, and
, is the linear fractional differential operator, newly defined as follows
where
and
For special values of the functions
h
and the parameters
n
,
α
,
m
and
λ
, we get known classes of starlike functions with respect to symmetric conjugate points. Inclusion relations, convolution properties and other results are given. Another related class is also defined.