Coefficient inequalities and Hankel determinant for a new subclass of q-starlike functions

In this study, for $0< q<1$ , we first introduce a function φ q ( τ ) = eqτ-1q ( 1-qτ ) and prove that φ q ( τ ) is convex univalent in the open unit disk U for all q∈ ( 0,0.32 ) . Further, using the subordination technique and considering q-difference operator, we define a new subclass Sφ(q) of q-starlike functions associated with a function 1+φ q ( τ ) , which is in the class 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 Sφ(q) .