Integral operators on Ma-Minda type starlike and convex functions

Keywords: Analytic functions Differential subordination Ma–Minda type starlike and convex functions Integral operators a b s t r a c t 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.