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

Nabadwip Sarkar; Pradip Das

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

Complex Variables 2026-07-14 v1

Authors: Nabadwip Sarkar , Pradip Das

Abstract

This paper is devoted to the study of the second Hankel determinant for normalized $\beta$ -spirallike mappings on the unit ball of a complex Banach space. Using the relationship between Banach-space holomorphic mappings and corresponding one-variable $\beta$ -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.

Keywords

Hankel determinants β-spirallike mappings complex Banach spaces holomorphic mappings sharp estimates coefficient inequalities

Cite

@article{arxiv.2607.12509,
  title  = {On Hankel Determinants of $β$-Spirallike Mappings in Complex Banach Spaces},
  author = {Nabadwip Sarkar and Pradip Das},
  journal= {arXiv preprint arXiv:2607.12509},
  year   = {2026}
}