Differential subordinations for functions with positive real part using admissibility conditions

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