Integral operators on Ma-Minda type starlike and convex functions

Two integral operators on the classes consisting of normalized p-valent Ma-Minda type starlike and convex functions are considered. Functions in these classes have the form zf′(z)/f(z)≺pφ(z) and 1+zf″(z)/f′(z)≺pφ(z) respectively, where φ is a convex function with φ(0)=1. It is shown that the first of these operators maps starlike functions into convex functions, while the convex mappings are shown to be closed under the second integral operator.