Sharp Results for a New Class of Analytic Functions Associated with the q-Differential Operator and the Symmetric Balloon-Shaped Domain

Abstract

In our current study, we apply differential subordination and quantum calculus to introduce and investigate a new class of analytic functions associated with the q-differential operator and the symmetric balloon-shaped domain. We obtain sharp results concerning the Maclaurin coefficients the second and third-order Hankel determinants, the Zalcman conjecture, and its generalized conjecture for this newly defined class of q-starlike functions with respect to symmetric points.

Keywords

• differential subordination
• analytic function
• q-starlike function
• symmetric points
• Zalcman conjecture
• Hankel determinant