NEW CHARACTERIZATION OF THE CLASS OF STARLIKE FUNCTIONS

Abstract. For analytic functions f ( z ) in the open unit disc D, an opera-tor N α ( f ( z )) relating with starlike functions is introduced. The object ofthe present paper is to discuss some properties of the operator N α ( f ( z )). 1. IntroductionLet Ω be the class of functions w ( z ) which are regular in the open unit discD = {z ∈ C ||z| α ( z ∈ D)for some α (0 5 α < 1). We denote by S ∗ ( α ) the subclass of A consisting ofall starlike functions of order