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

Sibel Yalçın | Zendy; Ali Ebadian | Zendy; S. Pourmohammad Azizi | Zendy

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

Author(s) -

Sibel Yalçın,

Ali Ebadian,

S. Pourmohammad Azizi

Publication year - 2021

Publication title -

ukrains’kyi matematychnyi zhurnal

Language(s) - English

Resource type - Journals

ISSN - 1027-3190

DOI - 10.37863/umzh.v73i2.94

Subject(s) - conjecture , convolution (computer science) , harmonic , mathematics , plane (geometry) , pure mathematics , computer science , geometry , physics , artificial intelligence , quantum mechanics , artificial neural network

UDC 517.5Recently, 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 and . Also, it has been proved only for . In this paper, by using of a new method, we settle this conjecture in the affirmative for all and . 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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