Abstract
Let κ be an analytic function in the open unit disc U in the complex plane with κ(0) = 1 . Then κ ∈ K(λ) if and only if κ(t) ≺ ϕλ(t) , where ≺ is a subordination relation and the function ϕλ(t): = (1+t)λ , for 0 < λ < 1 , maps U to a symmetric domain about the real axis in the right-half plane. This article finds the sharp radii of starlikeness for three classes of normalized analytic functions in the open unit disc. It also finds the solutions to first-order differential equations and utilizes these results together with the differential subordination developed by Miller and Mocanu to obtain the conditions so that some first-order differential relations associated with ϕλ are subordinate to certain Ma and Minda functions. Consequently, it provides sufficient conditions for the normalized analytic functions to belong to some established subclasses of starlike functions.