Sharp Bounds on the Third Hankel Determinants for Starlike and Convex Functions Associated with the Gregory Coefficients

Key Points

• This research aims to determine sharp bounds for the third Hankel determinant in specific classes of functions.
• Analyzed coefficients of Taylor series for starlike and convex functions.
• Calculated third Hankel determinants using Gregory coefficients.
• Compared results with existing literature to establish improvements.
• Established sharp bounds for the third Hankel determinant in both classes of functions.
• Showed that the new bounds are tighter than previously known results in literature.