Volume 48, Issue 3
The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts

J. Math. Study, 48 (2015), pp. 265-274.

Published online: 2015-09

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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

30D15, 30D99

ZMK900116@163.com (Mengkun Zhu)

huangXZ@hqu.edu.cn (Xinzhong Huang)

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@Article{JMS-48-265, author = {Zhu , Mengkun and Huang , Xinzhong}, title = {The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts}, journal = {Journal of Mathematical Study}, year = {2015}, volume = {48}, number = {3}, pages = {265--274}, 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.v48n3.15.05}, url = {http://global-sci.org/intro/article_detail/jms/9928.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 - 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 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. (2020). The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts. Journal of Mathematical Study. 48 (3). 265-274. doi:10.4208/jms.v48n3.15.05
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