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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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 2, pp. 283–288, February, 2021. Ukrainian DOI: 10.37863/umzh.v73i2.94.
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Yalçın, S., Ebadian, A. & Azizi, S. A Proof of a Conjecture on the Convolution of Harmonic Mappings and Some Related Problems. Ukr Math J 73, 329–336 (2021). https://doi.org/10.1007/s11253-021-01927-w
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DOI: https://doi.org/10.1007/s11253-021-01927-w