About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 404672, 7 pages
http://dx.doi.org/10.1155/2013/404672
Research Article

A Connection between Basic Univalence Criteria

Department of Mathematics, Faculty of Mathematics and Computer Science, “Transilvania” University of Braşov, 500091 Braşov, Romania

Received 23 January 2013; Accepted 25 June 2013

Academic Editor: Abdelaziz Rhandi

Copyright © 2013 Horiana Tudor. 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. W. Alexander, “Functions which map the interior of the unit circle upon simple regions,” Annals of Mathematics, vol. 17, no. 1, pp. 12–22, 1915. View at Publisher · View at Google Scholar · View at MathSciNet
  2. K. Noshiro, “On the theory of schlicht functions,” Journal of the Faculty of Science, Hokkaido University, vol. 1, pp. 129–155, 1934.
  3. S. E. Warschawski, “On the higher derivatives at the boundary in conformal mapping,” Transactions of the American Mathematical Society, vol. 38, no. 2, pp. 310–340, 1935. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Z. Nehari, “The Schwarzian derivative and schlicht functions,” Bulletin of the American Mathematical Society, vol. 55, pp. 545–551, 1949. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, vol. 29 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1969. View at MathSciNet
  6. S. Ozaki and M. Nunokawa, “The Schwarzian derivative and univalent functions,” Proceedings of the American Mathematical Society, vol. 33, no. 2, pp. 392–394, 1972. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Becker, “Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen,” Journal für die Reine und Angewandte Mathematik, vol. 255, pp. 23–43, 1972. View at Zentralblatt MATH · View at MathSciNet
  8. Z. Lewandowski, “On a univalence criterion,” L'Académie Polonaise des Sciences. Bulletin, vol. 29, no. 3-4, pp. 123–126, 1981. View at Zentralblatt MATH · View at MathSciNet
  9. N. N. Pascu, “On a univalence criterion. II,” in Itinerant Seminar on Functional Equations, Approximation and Convexity (Cluj-Napoca, 1985), vol. 85 of Preprint, pp. 153–154, Babeş-Bolyai University, Cluj-Napoca, Romania, 1985. View at MathSciNet
  10. M. C. Çağlar and H. Orhan, “Some generalizations on the univalence of an integral operator and quasiconformal extension,” Miskolc Mathematical Notes, vol. 14, no. 1, pp. 49–62, 2013.
  11. E. Deniz, D. Răducanu, and H. Orhan, “On an improvement of a univalence criterion,” Mathematica Balkanica, vol. 24, no. 1-2, pp. 33–39, 2010. View at Zentralblatt MATH · View at MathSciNet
  12. H. Ovesea, “A generalization of Lewandowski's univalence criterion,” Mathematica, vol. 37, no. 60, pp. 189–198, 1995. View at Zentralblatt MATH · View at MathSciNet
  13. H. Ovesea, “An univalence criterion and the Schwarzian derivative,” Novi Sad Journal of Mathematics, vol. 26, no. 1, pp. 69–76, 1996. View at Zentralblatt MATH · View at MathSciNet
  14. H. Tudor, “An extension of Ozaki and Nunokawa's univalence criterion,” Journal of Inequalities in Pure and Applied Mathematics, vol. 9, no. 4, article 117, 2008. View at Zentralblatt MATH · View at MathSciNet
  15. CH. Pommerenke, “Über die Subordination analytischer Funktionen,” Journal für die Reine und Angewandte Mathematik, vol. 218, pp. 159–173, 1965. View at Zentralblatt MATH · View at MathSciNet
  16. C. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, Germany, 1975. View at MathSciNet
  17. N. N. Pascu, “An improvement of Becker's univalence criterion,” in Proceedings of the Commemorative Session: Simion StoïloW, pp. 43–48, University of Braşov, Braşov, Romania, 1987. View at MathSciNet
  18. H. Tudor and S. Owa, “Univalence criteria concerned with Loewner chains of certain analytic functions,” Pan-American Mathematical Journal, vol. 22, no. 4, pp. 81–95, 2012.
  19. H. Ovesea-Tudor, “A condition for univalency,” Mathematica, vol. 47, no. 70, pp. 101–104, 2005. View at Zentralblatt MATH · View at MathSciNet