Let A be tile class of all analytic functions in the unit disk U such that f(0)=f′(0)−1=0. A function f∈A is called starlike with respect to 2n symmetric-conjugate points
if Rezf′(z)/fn(z)>0 for z∈U, where
fn(z)=12n∑k=0n−1[ω−kf(ωkz)+ωkf(ωkz˜)¯],
ω=exp(2πi/n]. This class is denoted by Sn*, and was studied in [1]. A sufficient condition for
starlikeness with respect to symmetric-conjugate points is obtained. In addition, images of some
subclasses of Sn* under the integral operator I:A→A, I(f)=F where
F(z)=c+1(g(z))c∫0zf(t)(g(t))c−1g′(t)dt, c>0
and g∈A is given are determined.