TY - JOUR
T1 - The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts
AU - Zhu , Mengkun
AU - Huang , Xinzhong
JO - Journal of Mathematical Study
VL - 1
SP - 23
EP - 32
PY - 2016
DA - 2016/03
SN - 49
DO - http://doi.org/10.4208/jms.v49n1.16.03
UR - https://global-sci.org/intro/article_detail/jms/985.html
KW - Harmonic mapping, coefficient estimate, distortion theorem, covering problem.
AB - <p style="text-align: justify;">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 $\mathbb{D}:=\{z:|z|&lt;1\}.$ 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.</p>