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arXiv · 2608.01087

Bohr-type inequalities with Fr\'{e}chet derivative and Area terms in Complex Banach spaces

Nabadwip Sarkar·Pradip Das
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Abstract

We establish new Bohr-type inequalities for holomorphic mappings from the unit ball of a complex Banach space into the closed unit disk. Using Fr\'{e}chet derivatives, Schwarz mappings of prescribed orders and area functionals, we obtain sharp Bohr radii characterized by explicit equations. We further prove a refined Bohr inequality involving derivative, coefficient and area terms and show that the corresponding radius is the unique positive solution of $r^m=(\sqrt{17}-3)/4$. The sharpness of the obtained radii and constants is also established. Our results extend several recent Bohr-type inequalities for bounded analytic functions on the unit disk to the setting of holomorphic mappings on complex Banach spaces.

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Nabadwip Sarkar, Pradip Das. 2026-08-02. Bohr-type inequalities with Fr\'{e}chet derivative and Area terms in Complex Banach spaces. https://arxiv.org/abs/2608.01087

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