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.

中文翻译：

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复值核$$ \ alpha $$α-调和映射的某些几何性质

我们称该类加权Laplace方程为复值核\（\ alpha \）-调和映射的解。本文研究了复值核\（\ alpha \）-调和映射的某些几何性质，例如面积，完全星形和完全凸度的阶数\（\ gamma \），\（\ gamma \ in [0， 1）\），进行探索。此外，对于一类给定的边界函数，获得了Radó-Kneser-Choquet型定理。