Third Hankel determinant for an inverse of a function associated with the exponential mapping

Key Points

• To determine the sharp upper bound on the third-order Hankel determinant for a subclass of normalized analytic functions related to the exponential function.
• Calculate the third-order Hankel determinant for coefficients of the inverse function.
• Analyze functions that lie within a specific subclass of normalized analytic functions.
• Estimate Zalcman functionals using similar techniques.
• Identified a precise upper bound for the third Hankel determinant.
• Demonstrated the relationship between the upper bound and the coefficients of the inverse function.
• Confirmed the applicability of results to Zalcman functionals.