Hankel, Toeplitz, Hermitian--Toeplitz Determinants and the Zalcman Functional for a Class of Biholomorphic Mappings on Complex Banach Spaces

Abstract

In this paper, we investigate the second Hankel determinant, Toeplitz determinants, Hermitian--Toeplitz determinants and the generalized Zalcman functional for a class of normalized biholomorphic mappings on complex Banach spaces. Motivated by recent results for the corresponding class of analytic functions in the unit disk, we establish Banach space analogues of these determinant estimates. Our results extend the one-variable inequalities of Allu, Lecko and Thomas \cite{ALT2022} to the setting of complex Banach spaces, thereby providing higher-dimensional counterparts for the class corresponding to $\mathcal{F}_{O}(λ)$.