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.v48n3.15.05

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 $f ∈ TL^α_H$ which are locally univalent harmonic mappings in the unit disk $\mathbb{D}:=\{z:|z| < 1\}$. Moreover, denoting the subclass $TS^α_H$ of the normalized univalent harmonic mappings, we also estimate the growth of $|f|,$ $f ∈ TS^α_H,$ and their covering theorems.

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Published

2015-09-02

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Issue

Vol. 48 No. 3 (2015)

Section

Articles

How to Cite

The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts. (2015). Journal of Mathematical Study, 48(3), 265-274. https://doi.org/10.4208/jms.v48n3.15.05