  Using Briot-Bouquet differential subordination technique, we establish
sufficient conditions for a class $\mathcal{S}^{*}_{\varrho}$ of starlike
functions associated with $\cosh\sqrt{z}.$ %Further, using admissibility
conditions, some differential subordination results for
$\mathcal{S}^{*}_{\varrho}$ are derived. Further, by employing admissibility
conditions, we obtain various differential subordination results pertaining to
the class $\mathcal{S}^{*}_{\varrho}.$
