On a sufficient condition for multivalently starlikeness (Q1340399)

A function \(f: f(z)= z^ q+ \sum^ \infty_{n= q+1} a_ n z^ n\), \(q\in N= \{1,2,3,\dots\}\) analytic in the unit disc \(E\) is called \(q\)- valently starlike with respect to the origin if and only if \(\text{Re } {zf'(z)\over f(z)}> 0\) in \(E\). The author obtains a sufficient condition for a function to be \(q\)-valently starlike by using the imaginary part of \({zf''(z)\over f'(z)}\). His result generalizes the one proved by \textit{P. Mocanu} for \(q= 1\) [Rev. Roum. Math. Pures Appl. 31, 231-235 (1986; Zbl 0607.30012)].