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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.

Linked References

  1. J. Clunie and T. Sheil-Small, “Harmonic univalent functions,” Annales Academiae Scientiarum Fennicae A, pp. 3–25, 1984. View at MathSciNet
  2. P. L. Duren, Univalent functions, vol. 259, Springer, New York, NY, USA, 1983. View at MathSciNet
  3. W. Hengartner and G. Schober, “On schlicht mappings to domains convex in one direction,” Commentarii Mathematici Helvetici, vol. 45, pp. 303–314, 1970. View at MathSciNet
  4. M. Dorff, “Convolutions of planar harmonic convex mappings,” Complex Variables, Theory and Application, vol. 45, no. 3, pp. 263–271, 2001. View at MathSciNet
  5. 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. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. R. Goodloe, “Hadamard products of convex harmonic mappings,” Complex Variables, Theory and Application, vol. 47, no. 2, pp. 81–92, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  7. L. L. Li and S. Ponnusamy, “Solution to an open problem on convolutions of harmonic mappings,” Complex Variables and Elliptic Equations, 2012. View at Publisher · View at Google Scholar
  8. L. L. Li and S. Ponnusamy, “Convolutions of slanted half-plane harmonic mappings,” Analysis, vol. 33, pp. 159–176, 2013. View at Publisher · View at Google Scholar
  9. Y. Abu-Muhanna and G. Schober, “Harmonic mappings onto convex domains,” Canadian Journal of Mathematics, vol. 39, no. 6, pp. 1489–1530, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  10. W. Hengartner and G. Schober, “Univalent harmonic functions,” Transactions of the American Mathematical Society, vol. 299, no. 1, pp. 1–31, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  11. C. Pommerenke, “On starlike and close-to-convex functions,” Proceedings of the London Mathematical Society, vol. 13, pp. 290–304, 1963. View at MathSciNet
  12. 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. View at Publisher · View at Google Scholar · View at MathSciNet