We first prove that the convolution of a normalized right half-plane mapping with another subclass of normalized right half-plane mappings with the dilatation [...] −z(a+z)/(1+az) is CHD (convex in the horizontal direction) provided [...] a=1 or [...] −1≤a≤0 . Secondly, we give a simply method to prove the convolution of two special subclasses of harmonic univalent mappings in the right half-plane is CHD which was proved by Kumar et al. [1, Theorem 2.2]. In addition, we derive the convolution of harmonic univalent mappings involving the generalized harmonic right half-plane mappings is CHD. Finally, we present two examples of harmonic mappings to illuminate our main results.
@article{bwmeta1.element.doi-10_1515_math-2016-0069,
author = {YingChun Li and ZhiHong Liu},
title = {Convolutions of harmonic right half-plane mappings},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {789-800},
zbl = {1352.31001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0069}
}
YingChun Li; ZhiHong Liu. Convolutions of harmonic right half-plane mappings. Open Mathematics, Tome 14 (2016) pp. 789-800. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0069/