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arXiv · 2608.01087

Bohr-type inequalities with Fréchet 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 Fréchet 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 Fréchet derivative and Area terms in Complex Banach spaces. https://arxiv.org/abs/2608.01087

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