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 - 3
SP - 265
EP - 274
PY - 2015
DA - 2015/09
SN - 48
DO - http://doi.org/10.4208/jms.v48n3.15.05
UR - https://global-sci.org/intro/article_detail/jms/9928.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 $f ∈ TL^α_H$&nbsp;which are locally univalent harmonic mappings
in the unit disk $\mathbb{D}:=\{z:|z| &lt; 1\}$. 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.</p>