The second Hankel determinant and the Fekete-Szegö functional for a subclass of analytic functions by using the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg" display="inline" id="d1e24"><mml:mi>q</mml:mi></mml:math>-Sălăge

The current study’s researchers create a new family of analytic functions in the open unit disk Λ by generalizing the q -difference operator. Our study lays a foundational understanding of the behavior of this functions. We establish sharp inequalities for the initial Taylor coefficients. We provide optimal estimates for solving the Fekete-Szegö problem and a second order Hankel determinant applicable to all functions in this class. Relevant links between the findings of this study and those from earlier investigations are indicated.