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On convolutions of harmonic univalent mappings convex in the direction of the real axis |
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| Authors: | Zhi-Gang Wang Zhi-Hong Liu and Ying-Chun Li |
| Institution: | School of Mathematics and Computing Science, Hunan First Normal University, Changsha 410205, Hunan, China,School of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan, China; College of Mathematics, Honghe University, Mengzi 661199, Yunnan, China and College of Mathematics, Honghe University, Mengzi 661199, Yunnan, China |
| Abstract: | In this paper, we show that convolutions of some planar harmonic mappings which convex in the direction of the real axis are also convex in the same direction. Furthermore, by means of the \textit{Mathematica} software, we present an example to illuminate the main result. |
| Keywords: | Harmonic univalent mapping convolution shear construction |
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