Sharpness Estimation of Hankel Determinants and Logarithmic Coefficients for a Family of Analytic Functions Related to a Lung-Shaped Domain

Key Points

• The research aims to analyze a new family of univalent analytic functions within lung-shaped domains, focusing on coefficient bounds and Hankel determinants.
• Applied subordination theory to analyze function properties.
• Established coefficient bounds for the first five coefficients of analytic functions.
• Derived estimates for Hankel determinants of orders two and three.
• Determined bounds for the first four logarithmic coefficients.
• Constructed extreme functions to demonstrate sharpness of bounds.
• Coefficient bounds for the first five coefficients were established effectively.
• Estimates for Hankel determinants of orders two and three were derived successfully.
• Sharp bounds for the first four logarithmic coefficients were determined.
• Zalcman functionals were bounded in the context of the study.

Abstract