- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 794108, 7 pages
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.
- J. Clunie and T. Sheil-Small, “Harmonic univalent functions,” Annales Academiae Scientiarum Fennicae A, pp. 3–25, 1984.
- P. L. Duren, Univalent functions, vol. 259, Springer, New York, NY, USA, 1983.
- W. Hengartner and G. Schober, “On schlicht mappings to domains convex in one direction,” Commentarii Mathematici Helvetici, vol. 45, pp. 303–314, 1970.
- M. Dorff, “Convolutions of planar harmonic convex mappings,” Complex Variables, Theory and Application, vol. 45, no. 3, pp. 263–271, 2001.
- M. Dorff, M. Nowak, and M. Wołoszkiewicz, “Convolutions of harmonic convex mappings,” Complex Variables and Elliptic Equations, vol. 57, no. 5, pp. 489–503, 2012.
- M. R. Goodloe, “Hadamard products of convex harmonic mappings,” Complex Variables, Theory and Application, vol. 47, no. 2, pp. 81–92, 2002.
- L. L. Li and S. Ponnusamy, “Solution to an open problem on convolutions of harmonic mappings,” Complex Variables and Elliptic Equations, 2012.
- L. L. Li and S. Ponnusamy, “Convolutions of slanted half-plane harmonic mappings,” Analysis, vol. 33, pp. 159–176, 2013.
- Y. Abu-Muhanna and G. Schober, “Harmonic mappings onto convex domains,” Canadian Journal of Mathematics, vol. 39, no. 6, pp. 1489–1530, 1987.
- W. Hengartner and G. Schober, “Univalent harmonic functions,” Transactions of the American Mathematical Society, vol. 299, no. 1, pp. 1–31, 1987.
- C. Pommerenke, “On starlike and close-to-convex functions,” Proceedings of the London Mathematical Society, vol. 13, pp. 290–304, 1963.
- J. S. Cheng, “A parallel algorithm for finding roots of a complex polynomial,” Journal of Computer Science and Technology, vol. 5, no. 1, pp. 71–81, 1990.