Second-Order Toeplitz Determinant for Quasi-Convex Mappings

Abstract

This paper presents sharp estimates for the second-order Toeplitz determinant whose entries are the coefficients of convex functions defined on the unit disk in $\mathbb{C}$. These estimates are further extended to a subclass of holomorphic mappings defined on the unit ball in a complex Banach space and on the unit polydisk in ${\mathbb{C}}^n$, which, as special cases, yield bounds for the classes of quasi-convex mappings of type $B$.