A new differential subordination technique for a subclass of starlike functions

In the present investigation, we employ a new technique to find several first and second order differential subordination implications involving the following starlike class associated with a bean shaped domain: \begin{equation*} $\mathcal{S}$^_{\mathfrak{B}}:=\left{f\in$\mathcal{S}$:\dfrac{zf’(z)}{f(z)}\prec\sqrt{1+\tanh{z}}=:\mathfrak{B}(z)\right}. \end{equation} Also, we give several applications stemming from our derived results.