A proof of a conjecture on convolution of harmonic mappings and some related problems
UDC 517.5 Recently, Kumar et al. proposed a conjecture concerning the convolution of a generalized right half-plane mapping with a vertical strip mapping. They have verified the above conjecture for $n=1,2,3$ and $4$. Also, it has been proved only for $\beta=\pi/2$. In this paper, by using of a new...
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| Date: | 2021 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/94 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
Recently, Kumar et al. proposed a conjecture concerning the convolution of a generalized right half-plane mapping with a vertical strip mapping. They have verified the above conjecture for $n=1,2,3$ and $4$. Also, it has been proved only for $\beta=\pi/2$. In this paper, by using of a new method, we settle this conjecture in the affirmative for all $n\in\mathbb{N}$ and $\beta\in(0,\pi)$. Moreover, we will use this method to prove some results on convolution of harmonic mappings. This new method simplifies calculations and shortens the proof of results remarkably. |
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| DOI: | 10.37863/umzh.v73i2.94 |