Neighborhoods and partial sums of certain subclass of starlike functions (Q394682)

In this paper the authors study a subclass of the class of starlike functions and give sufficient conditions when a neighborhood (concept introduced by S. Ruscheweyh) of a normalized analytic function belongs to that subclass. For a function \(f\) satisfying another (additional) condition, they give a sharp lower bound of \(\mathrm{Re} [f(z)/f_n(z)]\), where \(f_n\) is partial sum of \(f\).