Sharp Bounds on Hankel Determinants for Starlike Functions Defined by Symmetry with Respect to Symmetric Domains

This work investigates the behavior of the coefficients of analytic functions within certain subclasses characterized by inherent symmetric structures. By leveraging deep connections with functions exhibiting positive real part properties, the approach introduces a modern analytical framework that links the studied coefficients to those of auxiliary functions with regulated behavior. This connection allows for the derivation of sharp estimates and facilitates computational treatment. The proposed method builds upon certain classical and modern coefficient inequalities. The study focuses on obtaining precise bounds for specific determinant expressions associated with initial, inverse, and inverse logarithmic coefficients, all within a subclass of starlike functions exhibiting internal symmetry aligned with a recently introduced canonical structure. This symmetric perspective reveals how geometric properties can lead to refined quantitative outcomes that enhance contemporary analytic theory.