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 ∈ TLαH, which are locally univalent harmonic mappings in the unit disk $\mathbb{D}$:={z:|z| ‹ 1}. Moreover, denoting the subclass TSαH of the normalized univalent harmonic mappings, we also estimate the growth of |f|, f ∈ TSαH, 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)

  • BibTex
  • RIS
  • TXT
@Article{JMS-49-23, author = {Zhu , Mengkun and Huang , Xinzhong }, 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 ∈ TLαH, which are locally univalent harmonic mappings in the unit disk $\mathbb{D}$:={z:|z| ‹ 1}. Moreover, denoting the subclass TSαH of the normalized univalent harmonic mappings, we also estimate the growth of |f|, f ∈ TSαH, 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://dor.org/10.4208/jms.v49n1.16.03 UR - https://global-sci.org/intro/article_detail/jms/985.html KW - Harmonic mapping KW - coefficient estimate KW - distortion theorem KW - covering problem AB -

Some sharp estimates for coefficients, distortion and the growth order are obtained for harmonic mappings f ∈ TLαH, which are locally univalent harmonic mappings in the unit disk $\mathbb{D}$:={z:|z| ‹ 1}. Moreover, denoting the subclass TSαH of the normalized univalent harmonic mappings, we also estimate the growth of |f|, f ∈ TSαH, 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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