  Some sufficient conditions on certain constants which are involved in some
first, second and third order differential subordinations associated with
certain functions with positive real part like modified Sigmoid function,
exponential function and Janowski function are obtained so that the analytic
function p normalized by the condition p(0) = 1, is subordinate to Janowski
function. The admissibility conditions for Janowski function are used as a tool
in the proof of the results. As application, several sufficient conditions are
also computed for Janowski starlikeness.
