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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 794108, 7 pages
http://dx.doi.org/10.1155/2013/794108
Research Article

The Properties of a New Subclass of Harmonic Univalent Mappings

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

Received 21 July 2013; Accepted 25 August 2013

Academic Editor: Irena Lasiecka

Copyright © 2013 Zhi-Hong Liu and Ying-Chun Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduced a new subclass of univalent harmonic functions defined by the shear construction in the present paper. First, we showed that the convolutions of two special subclass harmonic mappings are convex in the horizontal direction. Secondly, we proved a necessary and sufficient condition for the above subclass of harmonic mappings to be convex in the horizontal direction. We also presented some basic examples of univalent harmonic functions explaining the behavior of the image domains.