Geodesic
Coefficient Estimates and Landau-Bloch's Constant for Planar Harmonic Mappings
Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 2
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The aim of this paper is to study the properties of planar harmonic mappings. The main results are as follows. First, by using the subordination of analytic functions, a sharp coefficient estimate is obtained and several applications are given. Then two results about Landau-Bloch's constant are proved: one for planar harmonic mappings and the other for $L(f)$, where $L$ represents the linear complex operator $L=z\frac{\partial}{\partial z} -\overline{z}\frac{\partial}{\partial \overline{z}}$ defined on the class of complex-valued $C^1$ functions in the plane and $f$ is an open harmonic mapping.
Classification : Primary: 30C65, 30C45; Secondary: 30C20. 
@article{BMMS_2011_34_2_a4,
     author = {Sh. Chen and S. Ponnusamy and X. Wang},
     title = {Coefficient {Estimates} and {Landau-Bloch's} {Constant} for {Planar} {Harmonic} {Mappings}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2011},
     volume = {34},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2011_34_2_a4/}
}
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%A X. Wang
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%D 2011
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Sh. Chen; S. Ponnusamy; X. Wang. Coefficient Estimates and Landau-Bloch's Constant for Planar Harmonic Mappings. Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2011_34_2_a4/