PreprintCC BY 4.0arXiv
Improved Bohr inequalities involving Fréchet derivatives associated with Holomorphic mappings in Banach spaces
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 Fréchet 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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BibTeX
@misc{sarkar2026improved,
title = {{Improved Bohr inequalities involving Fréchet derivatives associated with Holomorphic mappings in Banach spaces}},
author = {Nabadwip Sarkar and Pradip Das},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.25269},
eprint = {2607.25269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25269},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Improved Bohr inequalities involving Fréchet derivatives associated with Holomorphic mappings in Banach spaces
AU - Nabadwip Sarkar
AU - Pradip Das
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2607.25269
UR - https://arxiv.org/abs/2607.25269
AB - 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 Fréchet 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.
ER -