# Convolutions of harmonic right half-plane mappings

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 789-800
- ISSN: 2391-5455

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topYingChun 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 -

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