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Bohr Phenomenon for Locally Univalent Functions and Logarithmic Power Series

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Abstract

In this article we prove Bohr inequalities for sense-preserving K-quasiconformal harmonic mappings defined in the unit disk \({{\mathbb {D}}}\) and obtain the corresponding results for sense-preserving harmonic mappings. In addition, Bohr inequalities are established for uniformly locally univalent holomorphic functions, and for \(\log (f(z)/z)\) where f is univalent or inverse of a univalent function.

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Acknowledgements

The authors wish to record their sincere thanks to the anonymous referee for his/her insightful comments, which greatly helped to improve the quality of this article.

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  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Bappaditya Bhowmik & Nilanjan Das

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  1. Bappaditya Bhowmik
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  2. Nilanjan Das
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Correspondence to Bappaditya Bhowmik.

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Communicated by Pekka Koskela.

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The first author of this article would like to thank SERB, DST, India (Ref. No.- MTR/2018/001176) for its financial support through MATRICS Grant.

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Bhowmik, B., Das, N. Bohr Phenomenon for Locally Univalent Functions and Logarithmic Power Series. Comput. Methods Funct. Theory 19, 729–745 (2019). https://doi.org/10.1007/s40315-019-00291-y

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