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 ${\mathcal{S}}_{\varrho }^{\ast },$ consisting of starlike functions that are associated with $\varrho (z):=\cosh \sqrt{z}\mathrm{.}$ %Further, using admissibility conditions, some differential subordination results for ${\mathcal{S}}_{\varrho }^{\ast }$ are derived. Furthermore, by employing admissibility conditions, we obtain various differential subordination results pertaining to the class ${\mathcal{S}}_{\varrho }^{\ast }\mathrm{.}$