Table of Contents
International Scholarly Research Notices
Volume 2014, Article ID 327962, 6 pages
http://dx.doi.org/10.1155/2014/327962
Research Article

Fekete-Szegö Inequalities for Certain Classes of Biunivalent Functions

Department of Mathematics, Faculty of Arts and Science, Uludag University, Bursa, Turkey

Received 23 June 2014; Accepted 3 September 2014; Published 9 November 2014

Academic Editor: Cédric Join

Copyright © 2014 Şahsene Altınkaya and Sibel Yalçın. 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 of Grundlehren der Mathematischen Wissenschaften, 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 and J. G. Clunie, “Aspects of comtemporary complex analysis,” in Proceedings of the NATO Advanced Study Instute Held at University of Durham: July 1–20, 1979, Academic Press, New York, NY, USA, 1980. View at Google Scholar
  4. E. Netanyahu, “The minimal distance of the image boundary from the orijin 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
  5. D. A. Brannan and T. S. Taha, “On some classes of bi-univalent functions,” Studia Universitatis Babes-Bolyai Mathematica, vol. 31, no. 2, pp. 70–77, 1986. View at Google Scholar · View at MathSciNet
  6. S. Altinkaya and S. Yalcin, “Initial coefficient bounds for a general class of biunivalent functions,” International Journal of Analysis, vol. 2014, Article ID 867871, 4 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  7. O. Crisan, “Coefficient estimates for certain subclasses of bi-univalent functions,” General Mathematics Notes, vol. 16, no. 2, pp. 93–102, 2013. 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 MathSciNet · View at Scopus
  9. B. S. Keerthi and B. Raja, “Coefficient inequality for certain new subclasses of analytic bi-univalent functions,” Theoretical Mathematics & Applications, vol. 3, no. 1, pp. 1–10, 2013. View at Google Scholar
  10. N. Magesh and J. Yamini, “Coefficient bounds for certain subclasses of bi-univalent functions,” International Mathematical Forum. Journal for Theory and Applications, vol. 8, no. 25-28, pp. 1337–1344, 2013. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. 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 MathSciNet · View at Scopus
  12. 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 MathSciNet · View at Scopus
  13. 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 on Proceedings Lecture Notes for Analysis, I, pp. 157–169, International Press, Cambridge, Mass, USA, 1994. View at Google Scholar
  14. 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 Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. R. M. Ali, S. K. Lee, V. Ravichandran, and S. Supramanian, “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 MathSciNet · View at Scopus
  16. K. Sakaguchi, “On a certain univalent mapping,” Journal of the Mathematical Society of Japan, vol. 11, pp. 72–75, 1959. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. Z. G. Wang, C. Y. Gao, and S. M. Yuan, “On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points,” Journal of Mathematical Analysis and Applications, vol. 322, no. 1, pp. 97–106, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. V. Ravichandran, “Starlike and convex functions with respect to conjugate points,” Acta Mathematica, vol. 20, no. 1, pp. 31–37, 2004. View at Google Scholar · View at MathSciNet · View at Scopus
  19. P. Zaprawa, “On the Fekete-Szegö problem for classes of bi-univalent functions,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 21, no. 1, pp. 169–178, 2014. View at Google Scholar · View at MathSciNet
  20. C. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, Germany, 1975. View at MathSciNet