Some applications of differential subordination

Abstract

Let S a ( h ) denote the class of analytic functions f on the unit disc E with f (0) =0 = f ′ (0) −1 satisfying , where (a real), denotes the Hadamard product of K a with f , and h is a convex univalent function on E , with Re h > 0. Let . It is proved that F ε S a ( h ) whenever f ε S a ( h ) and also that for a ≥ 1. Three more such classes are introduced and studied here. The method of differential subordination due to Eenigenburg et al. is used.