关于类\\(\mathcal{S}_{car}^*\\)涉及对数系数与逆对数系数的Sharp Hankel行列式及Hermitian–Toeplitz行列式
Sharp Hankel and Hermitian--Toeplitz Determinants Involving Logarithmic and Inverse Logarithmic Coefficients for the class \(\mathcal{S}_{car}^*\)
AI总结：
本文针对与心脏线区域相关的星型函数类，推导了二阶对数系数与逆对数系数的Hankel行列式的sharp界，完整解决了三阶Hermitian–Toeplitz行列式的sharp极值问题，相关结果由极值实例验证。
AI中文摘要：
本文研究与心脏线区域相关的星型函数类的系数问题，推导了二阶对数系数与逆对数系数的Hankel行列式的sharp界，还通过给出三阶Hermitian–Toeplitz行列式的sharp上、下界，完整解决了该极值问题，所有结果均由极值实例验证所得估计的sharp性。
英文摘要：
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.
