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A convolution property of univalent harmonic right half-plane mappings

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Abstract

We consider the convolution of right half-plane harmonic mappings in the unit disk \(\mathbb {D}:=\{z\in \mathbb {C}:\, |z|<1\}\) with respective dilatations \( e^{i \alpha }(z + a)/(1 + a z)\) and \(-z\), where \(-1< a < 1\) and \(\alpha \in \mathbb {R}\). We prove that such convolutions are locally univalent and convex in the horizontal direction under certain condition.

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Acknowledgements

The second author thanks SERB-MATRICS for the support.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, West Bengal, 713209, India

    Md Firoz Ali

  2. School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Argul, Bhubaneswar, Odisha, 752050, India

    Vasudevarao Allu

  3. Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore Centre, 8th Mile Mysore Road, Bangalore, 560059, India

    Nirupam Ghosh

Authors
  1. Md Firoz Ali
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  2. Vasudevarao Allu
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  3. Nirupam Ghosh
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Correspondence to Vasudevarao Allu.

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Communicated by Adrian Constantin.

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Ali, M.F., Allu, V. & Ghosh, N. A convolution property of univalent harmonic right half-plane mappings. Monatsh Math 193, 729–736 (2020). https://doi.org/10.1007/s00605-020-01442-3

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  • DOI: https://doi.org/10.1007/s00605-020-01442-3

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