A proof of a conjecture on convolution of harmonic mappings and some related problems

  • S. Yalçın Bursa Uludag Univ., Turkey
  • A. Ebadian Urmia Univ., Iran
  • S. Azizi Payame Noor Univ., Tehran, Iran
Keywords: Harmonic convolutions, harmonic vertical strip mappings, harmonic half-plane mappings


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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How to Cite
Yalçın, S., A. Ebadian, and S. Azizi. “A Proof of a Conjecture on Convolution of Harmonic Mappings and Some Related Problems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 2, Feb. 2021, pp. 283 -88, doi:10.37863/umzh.v73i2.94.
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