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arXiv · 1605.02293

Geometric properties of $\log$-polyharmonic mappings

Jiaolong Chen·Bin Sheng·Xiaotao Wang
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Abstract

In this paper, a class of $\log$-polyharmonic mappings $\mathcal{L}_p\mathcal{H}$ together with its subclass $\mathcal{L}_p\mathcal{H}(G)$ in the unit disk $\mathbb{D}=\{z: |z|<1\}$ is introduced, and several geometrical properties such as the starlikeness, convexity and univalence are investigated. In particular, we consider the Goodman-Saff conjecture and prove that the conjecture is true in $\mathcal{L}_p\mathcal{H}(G)$.

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Jiaolong Chen, Bin Sheng, Xiaotao Wang. 2016-11-07. Geometric properties of $\log$-polyharmonic mappings. https://arxiv.org/abs/1605.02293

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