Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 640856, 6 pages
http://dx.doi.org/10.1155/2014/640856
Research Article

Initial Coefficients of Biunivalent Functions

1School of Mathematical Sciences, Universiti Sains Malaysia (USM), 11800 Penang, Malaysia
2Department of Mathematics, University of Delhi, Delhi 110 007, India

Received 24 January 2014; Accepted 12 March 2014; Published 8 April 2014

Academic Editor: Om P. Ahuja

Copyright © 2014 See Keong Lee 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. P. L. Duren, Univalent Functions, vol. 259, Springer, New York, NY, USA, 1983. View at MathSciNet
  2. M. Lewin, “On a coefficient problem for bi-univalent functions,” Proceedings of the American Mathematical Society, vol. 18, pp. 63–68, 1967. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. D. A. Brannan, J. Clunie, and W. E. Kirwan, “Coefficient estimates for a class of star-like functions,” Canadian Journal of Mathematics, vol. 22, pp. 476–485, 1970. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. E. Netanyahu, “The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in z<1,” Archive for Rational Mechanics and Analysis, vol. 32, pp. 100–112, 1969. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. A. Brannan and T. S. Taha, “On some classes of bi-univalent functions,” Universitatis Babeş-Bolyai. Studia. Mathematica, vol. 31, no. 2, pp. 70–77, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. R. M. Ali, S. K. Lee, V. Ravichandran, and S. Supramaniam, “The Fekete-Szegő coefficient functional for transforms of analytic functions,” Iranian Mathematical Society. Bulletin, vol. 35, no. 2, article 276, pp. 119–142, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. M. Ali, V. Ravichandran, and N. Seenivasagan, “Coefficient bounds for p-valent functions,” Applied Mathematics and Computation, vol. 187, no. 1, pp. 35–46, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  8. B. A. Frasin and M. K. Aouf, “New subclasses of bi-univalent functions,” Applied Mathematics Letters, vol. 24, no. 9, pp. 1569–1573, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. K. Mishra and P. Gochhayat, “Fekete-Szegö problem for a class defined by an integral operator,” Kodai Mathematical Journal, vol. 33, no. 2, pp. 310–328, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. T. N. Shanmugam, C. Ramachandran, and V. Ravichandran, “Fekete-Szegő problem for subclasses of starlike functions with respect to symmetric points,” Bulletin of the Korean Mathematical Society, vol. 43, no. 3, pp. 589–598, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. H. M. Srivastava, “Some inequalities and other results associated with certain subclasses of univalent and bi-univalent analytic functions,” in Nonlinear Analysis, vol. 68 of Springer Series on Optimization and Its Applications, pp. 607–630, Springer, Berlin, Germany, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. H. M. Srivastava, A. K. Mishra, and P. Gochhayat, “Certain subclasses of analytic and bi-univalent functions,” Applied Mathematics Letters, vol. 23, no. 10, pp. 1188–1192, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Q.-H. Xu, H.-G. Xiao, and H. M. Srivastava, “A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems,” Applied Mathematics and Computation, vol. 218, no. 23, pp. 11461–11465, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Q.-H. Xu, Y.-C. Gui, and H. M. Srivastava, “Coefficient estimates for a certain subclass of analytic and bi-univalent functions,” Applied Mathematics Letters, vol. 25, no. 6, pp. 990–994, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. G. Murugusundaramoorthy, N. Magesh, and V. Prameela, “Coefficient bounds for certain subclasses of bi-univalent function,” Abstract and Applied Analysis, vol. 2013, Article ID 573017, 3 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  16. H. Tang, G.-T. Deng, and S.-H. Li, “Coefficient estimates for new subclasses of Ma-Minda bi-univalent functions,” Journal of Inequalities and Applications, vol. 2013, article 317, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S. G. Hamidi, S. A. Halim, and J. M. Jahangiri, “Coefficent estimates for bi-univalent strongly starlike and Bazilevic functions,” International Journal of Mathematics Research, vol. 5, no. 1, pp. 87–96, 2013. View at Google Scholar
  18. S. Bulut, “Coefficient estimates for initial Taylor-Maclaurin coefficients for a subclass of analytic and bi-univalent functions defined by Al-Oboudi differential operator,” The Scientific World Journal, vol. 2013, Article ID 171039, 6 pages, 2013. View at Publisher · View at Google Scholar
  19. S. Bulut, “Coefficient estimates for a class of analytic and bi-univalent functions,” Novi Sad Journal of Mathematics, vol. 43, no. 2, pp. 59–65, 2013. View at Google Scholar
  20. N. Magesh, T. Rosy, and S. Varma, “Coefficient estimate problem for a new subclass of biunivalent functions,” Journal of Complex Analysis, vol. 2013, Article ID 474231, 3 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  21. H. M. Srivastava, G. Murugusundaramoorthy, and N. Magesh, “On certain subclasses of bi-univalent functions associated with Hohlov operator,” Global Journal of Mathematical Analysis, vol. 1, no. 2, pp. 67–73, 2013. View at Google Scholar
  22. M. Çağlar, H. Orhan, and N. Yağmur, “Coefficient bounds for new subclasses of bi-univalent functions,” Filomat, vol. 27, no. 7, pp. 1165–1171, 2013. View at Publisher · View at Google Scholar
  23. H. M. Srivastava, S. Bulut, M. C. Çağlar, and N. Yağmur, “Coefficient estimates for a general subclass of analytic and bi-univalent functions,” Filomat, vol. 27, no. 5, pp. 831–842, 2013. View at Publisher · View at Google Scholar
  24. S. S. Kumar, V. Kumar, and V. Ravichandran, “Estimates for the initial coefficients of bi-univalent functions,” Tamsui Oxford Journal of Information and Mathematical Science. In press.
  25. W. C. Ma and D. Minda, “A unified treatment of some special classes of univalent functions,” in Proceedings of the Conference on Complex Analysis (Tianjin, 1992), Conference Proceedings and Lecture Notes in Analysis, pp. 157–169, International Press, Cambridge, Mass, USA.
  26. R. M. Ali, S. K. Lee, V. Ravichandran, and S. Supramaniam, “Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions,” Applied Mathematics Letters, vol. 25, no. 3, pp. 344–351, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. A. W. Kędzierawski, “Some remarks on bi-univalent functions,” Annales Universitatis Mariae Curie-Skłodowska. Section A. Mathematica, vol. 39, no. 1985, pp. 77–81, 1988. View at Google Scholar · View at MathSciNet