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arXiv · 2312.15945

Bohr-type inequalities for classes of analytic maps and K-quasiconformal harmonic mappings

Molla Basir Ahamed·Sabir Ahammed
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Abstract

In this paper, a significant improvement has been achieved in the classical Bohr's inequality for the class $ \mathcal{B} $ of analytic self maps defined on the unit disk $ \mathbb{D} $. More precisely, we generalize and improve several Bohr-type inequalities by combining appropriate improved and refined versions of the classical Bohr's inequality with some methods concerning the area measure of bounded analytic functions in $ \mathcal{B} $. In addition, we obtain Bohr-type and Bohr-Rogosinski-type inequalities for the subordination class and also for the class of $ K $-quasiconformal harmonic mappings. All the results are proved to be sharp.

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Molla Basir Ahamed, Sabir Ahammed. 2023-12-26. Bohr-type inequalities for classes of analytic maps and K-quasiconformal harmonic mappings. https://arxiv.org/abs/2312.15945

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