Convolutions of harmonic right half-plane mappings

• Autorzy: YingChun Li , ZhiHong Liu
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Harmonic univalent mappings; Harmonic convolution; Generalized right half-plane mappings

Kategorie tematyczne

• 58E20: Harmonic maps , etc.
• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 789-800

Daty

wydano

2016-01-01

otrzymano

2016-03-22

zaakceptowano

2016-07-27

online

2016-10-20

Twórcy

autor

YingChun Li

• College of Mathematics, Honghe University, Mengzi 661199, Yunnan,,

autor

ZhiHong Liu

• College of Mathematics, Honghe University, Mengzi 661199, Yunnan,,
• School of Mathematics and Econometrics, Hunan University, Changsha 410082, Hunan,

Identyfikatory

DOI

10.1515/math-2016-0069