On partial sums of the Libera integral operator (Q1378706)

The authors prove that for any function \(f(z)=z +\sum^\infty_{k=2} a_kz^k\) univalent in the unit disc and any natural number \(n\geq 2\) the partial sums of the Libera operator \(S_n(z,f)=z+\sum^n_{k=2} 2/(k+1) a_kz^k\) are starlike in the disc \(\{z\mid | z|<3/8\}\).