In this study, for $0< q<1$ , we first introduce a function $\varphi _{q}\left ( \tau \right ) = \frac{e^{q\tau }-1}{q\left ( 1-q\tau \right ) }$ and prove that $\varphi _{q}\left ( \tau \right ) $ is convex univalent in the open unit disk $\mathcal{U}$ for all $q\in \left ( 0,0.32\right ) $ . Further, using the subordination technique and considering q-difference operator, we define a new subclass $S_{\varphi }^{\ast }(q)$ of q-starlike functions associated with a function $1+\varphi _{q}\left ( \tau \right ) $ , which is in the class $\mathcal{P}$ . Some new geometric properties, such as coefficient bounds, Feketo–Szego inequalities, and the upper bound of the second-order Hankel determinant, are investigated for the function h belonging to the class $S_{\varphi }^{\ast }(q)$ .
