Convolutions of harmonic right half-plane mappings

YingChun Li, and ZhiHong Liu. "Convolutions of harmonic right half-plane mappings." Open Mathematics 14.1 (2016): 789-800. <http://eudml.org/doc/287155>.

@article{YingChunLi2016,
abstract = {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) $ - z(a + z)/(1 + az)$ is CHD (convex in the horizontal direction) provided [...] a=1 $a = 1$ or [...] −1≤a≤0 $ - 1 \le a \le 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.},
author = {YingChun Li, ZhiHong Liu},
journal = {Open Mathematics},
keywords = {Harmonic univalent mappings; Harmonic convolution; Generalized right half-plane mappings; harmonic mappings; convolution},
language = {eng},
number = {1},
pages = {789-800},
title = {Convolutions of harmonic right half-plane mappings},
url = {http://eudml.org/doc/287155},
volume = {14},
year = {2016},
}

TY - JOUR
AU - YingChun Li
AU - ZhiHong Liu
TI - Convolutions of harmonic right half-plane mappings
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 789
EP - 800
AB - 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) $ - z(a + z)/(1 + az)$ is CHD (convex in the horizontal direction) provided [...] a=1 $a = 1$ or [...] −1≤a≤0 $ - 1 \le a \le 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.
LA - eng
KW - Harmonic univalent mappings; Harmonic convolution; Generalized right half-plane mappings; harmonic mappings; convolution
UR - http://eudml.org/doc/287155
ER -