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On stable harmonic mappings

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Abstract

Stable harmonic mappings were first introduced and studied by Hernández and Martín (Math Proc Camb Philos Soc 155:343–359, 2013). Continuing research in this direction, we first prove a result on stability of the integral transform of harmonic mappings. Afterwards, we proved that the harmonic convolution \((\varphi +\alpha \overline{\varphi })*f\) is a stable harmonic convex mapping for \(|\alpha |\le 1\), where \(\varphi \) is a convex univalent map and f is a stable harmonic convex map. Furthermore, we consider the meromorphic analogs of stable harmonic mappings and establish various interesting results for these new classes of mappings.

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Funding

The first author of this article would like to thank NBHM, DAE, India (Ref. No. 02011/10/2022 NBHM(RP)/R &D-II/9652) for its financial support. The second author of this article acknowledges the financial support from CSIR, HRDG, Govt. of India as a Ph.D. student (HRDG(CSIR), File No. 09/081(1308)/2017-EMR-I).

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

    Bappaditya Bhowmik & Santana Majee

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  1. Bappaditya Bhowmik
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  2. Santana Majee
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BB and SM have equally contributed.

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Correspondence to Bappaditya Bhowmik.

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Bhowmik, B., Majee, S. On stable harmonic mappings. Anal.Math.Phys. 12, 151 (2022). https://doi.org/10.1007/s13324-022-00760-z

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