Generalized Toeplitz determinants for Starlike Mappings in Several Complex Variables

Abstract

This paper establishes sharp bounds for the second and third-order Toeplitz determinants associated with starlike functions $f$ in the unit disk such that $f(z)-z$ has a zero of order $k+1$ at $z=0$. These bounds are further extended to starlike mappings defined on the unit ball in a complex Banach space and on bounded starlike circular domains in ${\mathbb{C}}^n$. The derived results generalize several known bounds as special cases.