  The association of subordination and special functions is used to find sharp
estimates on the parameter $\beta$ such that the analytic function $p(z)$ is
subordinate to certain functions having positive real part whenever $p(z)+\beta
z p'(z)$ is subordinate to the Janowski function. Further, when the traditional
approach of solving higher order differential subordination implications
failed, the concept of admissibility is employed to establish certain second
and third order differential subordination relations between the analytic
function $p$ and the functions associated with right half plane. As a sequel,
we demonstrated the starlikeness of various well-known analytic functions as
well.
