On Booth lemniscate and starlike functions

Let Delta be the open unit disk in the complex plane and A be the class of normalized analytic functions in . In this paper, we introduce and study the class BS(a) := f. A : z f (z) f (z) - 1 . z 1 - az2, z. , where 0 = a = 1 and. is the subordination relation. Some properties of this class like differential subordination, coefficient estimates and Fekete- Szego inequality associated with the k- th root transform are considered.