Abstract
We consider the analytic properties for sense-preserving univalent harmonic mappings on the unit disk D onto half planes \(\Omega =\{w: \text {Re} w> a, -\infty 0, f_{\bar{z}}(0)\in R\). By deriving an analytic representing formula for these univalent harmonic mappings, we obtain one necessary and sufficient condition for these sense-preserving univalent harmonic mappings to be harmonic K-quasiconformal mappings, we also obtain sharp coefficient estimates for these harmonic K-quasiconformal mappings. As an application, distortion theorems on length and area for their images are also obtained. Our results improve and generalize the one made by M. Ozturk.
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