On the Theorem of Wan for K-Quasiconformal Hyperbolic Harmonic Self Mappings of the Unit Disk
Mathematica Moravica, Tome 19 (2015) no. 1.

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We give a new glance to the theorem of Wan (Theorem 1.1) which is related to the hyperbolic bi-Lipschicity of the $K$-quasiconformal, $K\geq 1$, hyperbolic harmonic mappings of the unit disk $\mathbb{D}$ onto itself. Especially, if $f$ is such a mapping and $f(0) = 0$, we obtained that the following double inequality is valid $2|z|/(K+1) \leq |f(z)| \leq \sqrt{K|z|}$, whenever $z\in\mathbb{D}$.
Mots-clés : Hyperbolic metric, Harmonic mappings, Quasiconformal mappings 
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     author = {Miljan Kne\v{z}evi\'c},
     title = {On the {Theorem} of {Wan} for {K-Quasiconformal} {Hyperbolic} {Harmonic} {Self} {Mappings} of the {Unit} {Disk}},
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Miljan Knežević. On the Theorem of Wan for K-Quasiconformal Hyperbolic Harmonic Self Mappings of the Unit Disk. Mathematica Moravica, Tome 19 (2015) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2015_19_1_a6/