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Some Geometric Properties of Complex-Valued Kernel \(\alpha \)-Harmonic Mappings

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Abstract

We call the solution of a kind of weighted Laplace equation complex-valued kernel \(\alpha \)-harmonic mappings. In this paper, some geometric properties of the complex-valued kernel \(\alpha \)-harmonic mappings, such as area, fully starlikeness and fully convexity of order \(\gamma \), \(\gamma \in [0,1)\), are explored. Furthermore, for a class of given boundary function, the Radó–Kneser–Choquet-type theorem is obtained.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, China

    Bo-Yong Long & Qi-Han Wang

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  1. Bo-Yong Long
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  2. Qi-Han Wang
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Correspondence to Bo-Yong Long.

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Communicated by Rosihan M. Ali.

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Supported by NSFC (No. 11501001), Natural Science Foundation of Anhui Province (1908085MA18), Foundations of Anhui University (Y01002428, J01006023), China.

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Long, BY., Wang, QH. Some Geometric Properties of Complex-Valued Kernel \(\alpha \)-Harmonic Mappings. Bull. Malays. Math. Sci. Soc. 44, 2381–2399 (2021). https://doi.org/10.1007/s40840-021-01075-1

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  • DOI: https://doi.org/10.1007/s40840-021-01075-1

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