Abstract
In this paper, we introduce a new class $\mathscr{S}_{H} (k, γ; \phi)$ of harmonic quasiconformal mappings, where $k \in [0,1), γ \in [0,π)$ and $\phi$ is an analytic function. Sufficient conditions for the linear combinations of mappings in such classes to be in a similar class, and convex in a given direction, are established. In particular, we prove that the images of linear combinations in this class, for special choices of $γ$ and $\phi$, are convex.
Citation
Yong Sun. Antti Rasila. Yue-Ping Jiang. "Linear combinations of harmonic quasiconformal mappings convex in one direction." Kodai Math. J. 39 (2) 366 - 377, June 2016. https://doi.org/10.2996/kmj/1467830143
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