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arXiv · 2607.25269

Improved Bohr inequalities involving Fr\'{e}chet derivatives associated with Holomorphic mappings in Banach spaces

Nabadwip Sarkar·Pradip Das
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Abstract

Motivated by recent advances in derivative Bohr inequalities and their refinements, we investigate the Bohr phenomenon for holomorphic mappings in complex Banach spaces associated with Schwarz functions. We establish sharp Bohr-type inequalities involving higher-order Fr\'{e}chet derivatives for both $|F(z)|$ and its refined counterpart $|F(z)|^2$. The corresponding Bohr radii are determined and shown to be best possible. Our results provide affirmative answers to Questions 1.1 and 1.2 and extend several classical and recent Bohr inequalities from the unit disk to the setting of holomorphic mappings on Banach spaces.

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Nabadwip Sarkar, Pradip Das. 2026-07-28. Improved Bohr inequalities involving Fr\'{e}chet derivatives associated with Holomorphic mappings in Banach spaces. https://arxiv.org/abs/2607.25269

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