A Proof of a Conjecture on the Convolution of Harmonic Mappings and Some Related Problems

被引：0
作者：
S. Yalçın
A. Ebadian
S. Azizi
机构：
[1] Bursa Uludag University,
[2] Urmia University,undefined
[3] Payame Noor University,undefined
来源：
Ukrainian Mathematical Journal | 2021年 / 73卷
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摘要：
Recently, Kumar, et al. proposed a conjecture concerning the convolution of a generalized right half-plane mapping with a vertical strip mapping. They verified this conjecture for n = 1, 2, 3 and 4. Moreover, it was proved only for β = 𝜋/2. By using of a new method, we settle this conjecture in the affirmative way for all n 𝜖 ℕ and β 𝜖 (0, 𝜋). Moreover, we apply this method to prove some results on the convolutions of harmonic mappings. The proposed new method simplifies calculations and remarkably shortens the proof of the results.
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页码：329 / 336
页数：7
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