Sharp Hankel and Hermitian--Toeplitz Determinants Involving Logarithmic and Inverse Logarithmic Coefficients for the class \(\mathcal{S}_{car}^*\)

Nabadwip Sarkar; Pradip Das

Sharp Hankel and Hermitian--Toeplitz Determinants Involving Logarithmic and Inverse Logarithmic Coefficients for the class \(\mathcal{S}_{car}^*\)

Complex Variables 2026-08-06 v1

Authors: Nabadwip Sarkar , Pradip Das

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.

Keywords

starlike function Hankel determinant Toeplitz determinant logarithmic coefficient inverse coefficient sharp bound

Cite

@article{arxiv.2608.05915,
  title  = {Sharp Hankel and Hermitian--Toeplitz Determinants Involving Logarithmic and Inverse Logarithmic Coefficients for the class \(\mathcal{S}_{car}^*\)},
  author = {Nabadwip Sarkar and Pradip Das},
  journal= {arXiv preprint arXiv:2608.05915},
  year   = {2026}
}