Integral Transforms of Certain Subclasses of Analytic Functions

Let A be the class of normalized analytic functions in the unit disk and define the class P Ž . f A Re ei ŽŽ1 . f Ž z . z f Ž z . .4 0, z 4 . For a function f A we define the integral transform 1 f Žtz . V Ž f .Ž z . H Žt . dt , t 0 where is a real-valued, nonnegative weight function with H1 Žt. dt 1. For 0 f P Ž . we will find conditions such that V Ž f . is starlike and also such that V Ž f . P Ž .. We also discuss how to write the integral transform as a convolu- tion with a 2 F1 hypergeometric function.