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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 4732704, 11 pages
http://dx.doi.org/10.1155/2016/4732704
Research Article

Research on Geometric Mappings in Complex Systems Analysis

Yanyan Cui,1,2 Chaojun Wang,1 and Sifeng Zhu1

1College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466001, China
2College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei 050016, China

Received 16 June 2016; Accepted 1 November 2016

Academic Editor: Allan C. Peterson

Copyright © 2016 Yanyan Cui et al. 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. C. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, Germany, 1975. View at MathSciNet
  2. H. Cartan, “Sur la possibilite d’entendre aux functions de plusieurs variables complexes la theorie des functions univalents,” in Lecons sur les Functions Univalents on Mutivalents, P. Montel, Ed., Gauthier-Villar, Paris, France, 1933. View at Google Scholar
  3. R. W. Barnard, C. H. FitzGerald, and S. Gong, “A distortion thoerem for biholomorphic mappings in C2,” Transactions of the American Mathematical Society, vol. 344, pp. 902–924, 1994. View at Google Scholar
  4. T. S. Liu and W. J. Zhang, “A distortion thoerem for biholomorphic convex mappings in Cn,” Chinese Journal of Contemporary Mathematics, vol. 20, no. 3, pp. 421–430, 1999. View at Google Scholar
  5. S. Gong, S. K. Wang, and Q. H. Yu, “Biholomorphic convex mappings of ball in Cn,” Pacific Journal of Mathematics, vol. 161, no. 2, pp. 287–306, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  6. S. Gong and T. S. Liu, “Distortion theorems for biholomorphic convex mappings on bounded convex circular domains,” Chinese Annals of Mathematics, Series B, vol. 20, no. 3, pp. 297–304, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. I. Graham and D. Varolin, “Bloch constants in one and several variables,” Pacific Journal of Mathematics, vol. 174, no. 2, pp. 347–357, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. P. L. Duren, Univalent Functions, Springer, New York, NY, USA, 1983.
  9. T. H. Gronwall, “Some remarks on conformal representation,” Annals of Mathematics, vol. 16, no. 1–4, pp. 72–76, 1914/15. View at Publisher · View at Google Scholar · View at MathSciNet
  10. M. I. Robertson, “On the theory of univalent functions,” Annals of Mathematics, vol. 37, no. 2, pp. 374–408, 1936. View at Publisher · View at Google Scholar · View at MathSciNet
  11. A. V. Boyd, “Coefficient estimates for starlike functions of order α,” Proceedings of the American Mathematical Society, vol. 17, pp. 1016–1018, 1966. View at Google Scholar · View at MathSciNet
  12. H. Silverman, “Univalent functions with negative coefficients,” Proceedings of the American Mathematical Society, vol. 51, pp. 109–116, 1975. View at Publisher · View at Google Scholar · View at MathSciNet
  13. H. M. Srivastava and S. Owa, “Certain subclasses of starlike functions, I,” Journal of Mathematical Analysis and Applications, vol. 161, no. 2, pp. 405–415, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. K. A. Roper and T. J. Suffridge, “Convex mappings on the unit ball of Cn,” Journal d'Analyse Mathematique, vol. 65, pp. 333–347, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. I. Graham and G. Kohr, “Univalent mappings associated with the Roper-Suffridge extension operator,” Journal d'Analyse Mathématique, vol. 81, pp. 331–342, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  16. S. Gong and T. S. Liu, “The generalized Roper-Suffridge extension operator,” Journal of Mathematical Analysis and Applications, vol. 284, no. 2, pp. 425–434, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. G. Kohr, “Loewner chains and a modification of the Roper-Suffridge extension operator,” Mathematica, vol. 71, no. 1, pp. 41–48, 2006. View at Google Scholar · View at MathSciNet
  18. J. R. Muir, “A class of Loewner chain preserving extension operators,” Journal of Mathematical Analysis and Applications, vol. 337, no. 2, pp. 862–879, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  19. Y. H. Zhao, Almost Starlike Mappings of Complex Order λ on the Unit Ball of a Complex Banach Space, Zhejiang Normal University, Jinhua, China, 2013.
  20. L. V. Ahlfors, Complex Analysis, McGraw-Hill, New York, NY, USA, 3rd edition, 1978. View at MathSciNet
  21. L. Bieberbach, “Uber einige extremal problem in gebiete der konformen abbildung,” Mathematische Annalen, vol. 77, no. 2, pp. 153–172, 1916. View at Publisher · View at Google Scholar
  22. T. Hayami, S. Owa, and H. M. Srivastava, “Coefficient inequalities for certain classes of analytic and univalent functions,” Journal of Inequalities in Pure and Applied Mathematics, vol. 8, no. 4, pp. 1–10, 2007. View at Google Scholar · View at MathSciNet
  23. M. S. Liu and Y. C. Zhu, “Generalized Roper-Suffridge operators on bounded and complete Reinhardt domains,” Science in China, vol. 37, no. 10, pp. 1193–1206, 2007. View at Google Scholar
  24. Y. Y. Cui and C. J. Wang, “The generalized Roper-Suffridge extension operators in complex Banach space,” Journal of Mathematics, vol. 34, no. 3, pp. 515–520, 2014. View at Google Scholar