Sharp Hankel and Hermitian--Toeplitz Determinants Involving Logarithmic and Inverse Logarithmic Coefficients for the class \(S_car^*\)

2026/08/06 by Nabadwip Sarkar, Pradip Das
Mathematics · #math.CV

paper · pdf

arxiv created 2026/08/06 · arxiv updated 2026/08/07

Abstract

This paper focuses on coefficient problems for the class of starlike functions related to a cardioid region. We derive sharp bounds for the Hankel determinants of logarithmic coefficients and logarithmic inverse coefficients of order two. Additionally, we completely solve the extremal problem for the third-order Hermitian--Toeplitz determinant by providing its sharp upper and lower bounds. All results are supported by extremal examples demonstrating the sharpness of the obtained estimates.

Citations

• SECOND HANKEL DETERMINANT FOR LOGARITHMIC INVERSE COEFFICIENTS OF CONVEX AND STARLIKE FUNCTIONS
• SHARP BOUNDS OF SOME COEFFICIENT FUNCTIONALS OVER THE CLASS OF FUNCTIONS CONVEX IN THE DIRECTION OF THE IMAGINARY AXIS
• Logarithmic coefficients problems in families related to starlike and convex functions
• Logarithmic coefficients of the inverse of univalent functions
• Starlike functions associated with a cardioid
• Logarithmic coefficients of some close-to-convex functions
• A general approach to the Fekete-Szegö problem
• A proof of the Bieberbach conjecture
• Early coefficients of the inverse of a regular convex function
• Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I