On Hankel Determinants of $β$-Spirallike Mappings in Complex Banach Spaces

Abstract

This paper is devoted to the study of the second Hankel determinant for normalized $β$-spirallike mappings on the unit ball of a complex Banach space. Using the relationship between Banach-space holomorphic mappings and corresponding one-variable $β$-spirallike functions, we first establish sharp estimates for the initial homogeneous expansion coefficients. These coefficient inequalities are subsequently applied to derive a sharp bound for the second Hankel determinant.