Volume 49, Issue 1
The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts

Mengkun Zhu & Xinzhong Huang

J. Math. Study, 49 (2016), pp. 23-32.

Published online: 2016-03

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  • 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.

  • Keywords

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

  • AMS Subject Headings

30D15, 30D99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ZMK900116@163.com (Mengkun Zhu)

huangXZ@hqu.edu.cn (Xinzhong Huang)

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  • RIS
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@Article{JMS-49-23, author = {Mengkun and Zhu and ZMK900116@163.com and 7106 and School of Mathematical Science, Huaqiao University, Quanzhou 362021, Fujian, P.R. China and Mengkun Zhu and Xinzhong and Huang and huangXZ@hqu.edu.cn and 7107 and School of Mathematical Science, Huaqiao University, Quanzhou 362021, Fujian, P.R. China and Xinzhong Huang}, title = {The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts}, journal = {Journal of Mathematical Study}, year = {2016}, volume = {49}, number = {1}, pages = {23--32}, 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n1.16.03}, url = {http://global-sci.org/intro/article_detail/jms/985.html} }
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 -

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.

Mengkun Zhu & Xinzhong Huang. (2019). The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts. Journal of Mathematical Study. 49 (1). 23-32. doi:10.4208/jms.v49n1.16.03
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