On Sufficient Conditions for the class $S^*_\cosh\sqrt{z}$

Using differential subordination technique, such as Briot-Bouquet and others, we establish sufficient conditions for functions to be in a class $\mathcal{S}^{*}_{\varrho},$ consisting of starlike functions that are associated with $\varrho(z):=\cosh \sqrt{z}.$ %Further, using admissibility conditions, some differential subordination results for $\mathcal{S}^{*}_{\varrho}$ are derived. Furthermore, by employing admissibility conditions, we obtain various differential subordination results pertaining to the class $\mathcal{S}^{*}_{\varrho}.$