关于复Banach空间中β-螺旋状映射的Hankel行列式
On Hankel Determinants of $β$-Spirallike Mappings in Complex Banach Spaces
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中文总结 AI 辅助
研究复Banach空间单位球上归一化β-螺旋状映射的第二个Hankel行列式，利用Banach空间全纯映射与单变量β-螺旋状函数关系，先建立初始齐次展开系数估计，进而得出第二个Hankel行列式的精确界。
中文摘要 AI 辅助
本文致力于研究复Banach空间单位球上归一化β-螺旋状映射的第二个Hankel行列式。利用Banach空间全纯映射与相应单变量β-螺旋状函数的关系，首先建立了初始齐次展开系数的精确估计。随后应用这些系数不等式得出第二个Hankel行列式的精确界。
英文摘要
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.
