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Landau and Bloch constants for meromorphic functions

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Abstract

Let \({\mathbb D}\) be the open unit disc in the complex plane, and let \({\mathcal {A}}(p)\) be the class of all functions f holomorphic in \({\mathbb D}\setminus \{p\}\) having a simple pole at \(z=p\in (0,1)\) with \(f'(0)\ne 0.\) In this article, we present lower estimates of the Landau and the Bloch constants for functions in \({\mathcal A}(p)\) in the Euclidean metric. We also improve these estimates of the Landau and the Bloch constants by considering an interesting subclass of \({\mathcal A}(p)\).

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Acknowledgements

The authors thank Karl-Joachim Wirths and the referee for their suggestions and careful reading of the manuscript.

Funding

B. Bhowmik of this article would like to thank SERB, India for its financial support through Core Research Grant (Ref. No.-CRG/2022/001835). S. Sen would like to thank the financial support from CSIR, HRDG, India (Ref. No.-09/081(1389)/2019-EMR-I).

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

    Bappaditya Bhowmik & Sambhunath Sen

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  1. Bappaditya Bhowmik
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  2. Sambhunath Sen
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Correspondence to Bappaditya Bhowmik.

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Bhowmik, B., Sen, S. Landau and Bloch constants for meromorphic functions. Monatsh Math 201, 359–373 (2023). https://doi.org/10.1007/s00605-023-01839-w

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