Open AccessA proof of a conjecture on convolution of harmonic mappings and some related problems
Author(s) -
Sibel Yalçın,
Ali Ebadian,
Saman Azizi
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
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.