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Univalency of Convolutions of Univalent Harmonic Right Half-plane Mappings by Liu, Zhihong; Ponnusamy, Saminathan is a scholarly article available to read on EtoBox.

What is Univalency of Convolutions of Univalent Harmonic Right Half-plane Mappings about?

We consider the convolution of half-plane harmonic mappings with respective dilatations $(z+a)/(1+az)$ and $e^{i\theta}z^{n}$, where $-1<a<1$ and $\theta\in\mathbb{R},n\in\mathbb{N}$. We prove that such convolutions are locally univalent for $n=1$, which solves an open problem of Dorff et. al (see \cite[Problem~3.26]{Bshouty2010}). Moreover, we provide some numerical computations to illustrate that such convolutions are not univalent for $n\geq 2$.

Author

Liu, Zhihong; Ponnusamy, Saminathan

Published

2016

Language

EN