Second-Order Toeplitz Determinant for Starlike Mappings in One and Higher Dimensions

Abstract

The present work establishes sharp estimates for second-order Toeplitz determinant, given by \(\vert a_3^2 -a_4^2\vert \), for the Ma-Minda class of starlike functions. These results are further extended to higher dimensions by deriving sharp bounds for a subclass of holomorphic mappings defined on the unit ball in a complex Banach space and the unit polydisc in \(\mathbb {C}^n\), leading to corresponding estimates for second-order Toeplitz determinants for various subclasses of univalent mappings in several complex variables.