Toeplitz Determinants for Inverse Functions and their Logarithmic Coefficients Associated with Ma-Minda Classes

Abstract: The classes of analytic univalent functions on the unit disk defined by $$ \mathcal{S}^*(\varphi)= \bigg{ f \in \mathcal{A}: \frac{z f'(z)}{f(z)} \prec \varphi(z)\bigg}$$ and $$ \mathcal{C}(\varphi)=\bigg{ f \in \mathcal{A}: 1 + \frac{z f''(z)}{f'(z)} \prec \varphi(z)\bigg} $$ generalize various subclasses of starlike and convex functions, respectively. In this paper, sharp bounds are established for certain Toeplitz determinants constructed over the coefficients and logarithmic coefficients of inverse functions belonging to $\mathcal{S}^*(\varphi)$ and $\mathcal{C}(\varphi)$. Since these classes covers many well-known subclasses, the derived bounds are directly applicable to them as well.