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Construction of harmonic univalent mappings convex in one direction

ZhiGang WANG, Lei SHI, YuePing JIANG
2014 Scientia Sinica Mathematica  

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2020 pre-print arXiv:2003.04455v1 fatcat:yyt2v5hkhrcjtdd2jdd3y56otm
In the present paper, we derive several conditions of linear combinations and convolutions of harmonic mappings to be univalent and convex in one direction, one of them gives a partial answer to an open problem proposed by Dorff. The results presented here provide extensions and improvements of those given in some earlier works. Several examples of univalent harmonic mappings convex in one direction are also constructed to demonstrate the main results.
doi:10.1360/012013-180 fatcat:yjf236k6fbditppu6bxnmfk2g4
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ZhiGang WANG, Lei SHI, YuePing JIANG. "Construction of harmonic univalent mappings convex in one direction." Scientia Sinica Mathematica 44.2 (2014) 139