Radius of Starlikeness for Classes of Analytic Functions

Abstract

We consider normalized analytic function f on the open unit disk for which either $$Ref(z)/g(z)>0$$ , $$|f(z) /g(z) - 1|<1$$ or $$Re(1-z^2) f(z) /z>0$$ for some analytic function g with $$Re(1-z^2) g(z) /z>0$$ . We have obtained the radii for these functions to belong to various subclasses of starlike functions. The subclasses considered include the classes of starlike functions of order $$\alpha $$ , lemniscate starlike functions and parabolic starlike functions.