Second-Order Toeplitz Determinant for Starlike Mappings in One and Higher Dimensions

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发表日期：

2025年6月29日

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Surya Giri

摘要

The present work establishes sharp estimates for second-order Toeplitz determinant, given by $\vert a_3^2 -a_4^2\vert $ $| a_{3}^{2} - a_{4}^{2} |$ , for the Ma-Minda class of starlike functions. These results are further extended to higher dimensions by deriving sharp bounds for a subclass of holomorphic mappings defined on the unit ball in a complex Banach space and the unit polydisc in $\mathbb {C}^n$ $C^{n}$ , leading to corresponding estimates for second-order Toeplitz determinants for various subclasses of univalent mappings in several complex variables.