On a criterion for multivalently starlikeness (Q1362810)

Let \(S(p)\) be the class of functions \(f:f(z)= z^p+ \sum^\infty_{n=p+1} a_nz^n\) analytic in the unit disc \(E\) and satisfying \(\text{Re} {zf'(z) \over f(z)} >0\) for \(z\in E\). \(f\in S(p)\) is called a \(p\)-valently starlike function in \(E\). In this paper a counter example is given to show that the main theorem of [\textit{M. Nunokowa}, Tsukuba J. Math. 18, No. 1, 131-134 (1994; Zbl 0812.30005)] contains an error and then some sufficient conditions are obtained for the class \(S(p)\).