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Convolutions of harmonic right half-plane mappings

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Li Y., Liu Z.

Open Mathematics

2016

tom 14

nr 1

789-800

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.

Ograniczanie wyników

1 Open Mathematics

1 Li Y.

1 Liu Z.

1 2016

Wyniki wyszukiwania

Convolutions of harmonic right half-plane mappings