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Radius of Convexity for Analytic Part of Sense-Preserving Harmonic Mappings

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Abstract

Given a sense-preserving harmonic function \(f=h+\bar{g}\) defined in the open unit disk, the radius of convexity for the analytic part h is determined under various prescribed conditions on the associated analytic function \(\phi _f=h-g\). Moreover, the radius of starlikeness and convexity for the analytic part of harmonic Koebe function is also computed. All the obtained results are sharp.

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Acknowledgements

The first author is supported by a Senior Research Fellowship from the Council of Scientific and Industrial Research (CSIR), New Delhi, with File No. 09/045(1515)/2017-EMR-I. The authors are thankful to the referees for their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Ankur Raj

  2. Department of Mathematics, Ramanujan College, University of Delhi, Delhi, 110019, India

    Sumit Nagpal

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  1. Ankur Raj
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  2. Sumit Nagpal
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Correspondence to Sumit Nagpal.

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Communicated by See Keong Lee.

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Raj, A., Nagpal, S. Radius of Convexity for Analytic Part of Sense-Preserving Harmonic Mappings. Bull. Malays. Math. Sci. Soc. 45, 2665–2679 (2022). https://doi.org/10.1007/s40840-022-01322-z

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  • DOI: https://doi.org/10.1007/s40840-022-01322-z

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