Differential subordination for certain strongly starlike functions.

We consider a subclass S L ∗ (λ) of starlike functions f satisfying the subordination z f ′ (z) / f (z) ≺ φ (z) where the function φ defined by φ (z) = (1 + z) λ , 0 < λ ≤ 1 , maps the open unit disk in the complex plane to a domain symmetric with respect to real axis in the right-half plane. Applying the admissibility condition technique in the theory of differential subordination developed by Miller and Mocanu, we investigate various subordination for functions to belong this class. As applications, we present several sufficient conditions of normalized analytic functions to be in this class. [ABSTRACT FROM AUTHOR]