Hermitian Toeplitz determinants for the inverse of several univalent functions

Let A denote the class of functions $f$ of form $f\left(z\right)=z+\sum _{n=2}^{\mathrm{\infty }}{a}_n{z}^n$, which are analytic in the unit disk $\mathrm{\Delta }=\{z:|z|<1\}$. Let $S^{\ast }$( $K$, $RT$ and $T$ resp.) denote the class of functions $f\in A$ such that $\mathrm{R}\mathrm{e}\left\{\frac{z{f}^{\mathrm{\prime }}\left(z\right)}{f\left(z\right)}\right\}>0$ ( $\mathrm{R}\mathrm{e}\{1+\frac{z{f}^{\mathrm{\prime }\mathrm{\prime }}\left(z\right)}{f^{\mathrm{\prime }}\left(z\right)}\}>0$, $\mathrm{R}\mathrm{e}\left\{f^{\mathrm{\prime }}\right(z\left)\right\}>0$ and $\mathrm{R}\mathrm{e}\left\{\frac{f\left(z\right)}{z}\right\}>0$ resp.) in $\mathrm{\Delta }$. In the present paper, we determine the sharp bounds for $\left|{\mathit{T}}_{2,1}\left(f^{-1}\right)\right|,\left|{\mathit{T}}_{3,1}\left(f^{-1}\right)\right|$ for functions $f$ in the classes $S^{\ast }$, $K$, $RT$ and $T$.