  For a normalised analytic function f defined on the open unit disk in the
complex plane, we determine several sufficient conditions for starlikeness in
terms of the quotients Q_{ST}:=zf'(z)/f(z), Q_{CV}:=1+zf"(z)/f'(z) and the
Schwarzian derivative Q_{SD}:=z^2((f"(z)/f'(z))'-(f"(z)/f'(z))^2/2)$. These
conditions were obtained by using the admissibility criteria of starlikeness in
the theory of second order differential subordination.
