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arXiv · 1511.04642

Landau's theorems for certain biharmonic mappings

Ming-Sheng Liu·Zhi-Wen Liu·Yu-Can Zhu
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Abstract

Let $f(z)=h(z)+\overline{g(z)}$ be a harmonic mapping of the unit disk $U$. In this paper, the sharp coefficient estimates for bounded planar harmonic mappings are established, the sharp coefficient estimates for normalized planar harmonic mappings with $|h(z)|+|g(z)|\leq M$ are also provided. As their applications, Landau's theorems for certain biharmonic mappings are provided, which improve and refine the related results of earlier authors.

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Ming-Sheng Liu, Zhi-Wen Liu, Yu-Can Zhu. 2015-11-15. Landau's theorems for certain biharmonic mappings. https://arxiv.org/abs/1511.04642

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