The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts

Authors

  • Mengkun Zhu School of Mathematical Science, Huaqiao University, Quanzhou 362021, Fujian, P.R. China
  • Xinzhong Huang School of Mathematical Science, Huaqiao University, Quanzhou 362021, Fujian, P.R. China

DOI:

https://doi.org/10.4208/jms.v49n1.16.03

Keywords:

Harmonic mapping, coefficient estimate, distortion theorem, covering problem.

Abstract

Some sharp estimates for coefficients, distortion and the growth order are obtained for harmonic mappings $f \in TL^{\alpha}_H,$ which are locally univalent harmonic mappings in the unit disk $\mathbb{D}:=\{z:|z|<1\}.$ Moreover, denoting the subclass $TS^{\alpha}_H$ of the normalized univalent harmonic mappings, we also estimate the growth of $|f|,$ $f \in TS^α_H,$ and their covering theorems.

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Published

2018-08-16

Issue

Vol. 49 No. 1 (2016)

Section

Articles