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Open Mathematics

2016 | 14 | 1 | 789-800

Convolutions of harmonic right half-plane mappings

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.

EN

789-800

wydano
2016-01-01
otrzymano
2016-03-22
zaakceptowano
2016-07-27
online
2016-10-20

Twórcy

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