On a Solution of a Particular Case of Aliaga-Tuneski Question

Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 26)

Abstract

Z. Nehari found sufficient conditions implying univalence of analytic functions, expressed in terms of the Schwarzian derivative. His theorem had been used by us to generate additional families of conditions for univalence, depending on parameters.

Recently, Aliaga and Tuneski used the method of selecting parameters to find a new criterion for univalence of analytic functions. However, they presented determining specific suitable values of the parameters and their precise domain of admissibility for this family as an open question.

In what follows we obtain additional information about the exact domain of possible parameters in the family of criteria studied by Aliaga and Tuneski.

Keywords

Univalent functions Univalence criteria 

Mathematics Subject Classification

30C55 

References

  1. 1.
    Aharonov, D., Elias, U.: Univalence criteria depending on parameters. Anal. Math. Phys. 4, 23–34 (2014)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Aharonov, D., Elias, U.: Sufficient conditions for univalence of analytic functions. 1–30, (2013). arXiv:1303.0982v1 [math.CV]Google Scholar
  3. 3.
    Aharonov, D., Elias, U.: Sufficient conditions for univalence of analytic functions. J. Anal. 22, 1–11 (2014)MathSciNetMATHGoogle Scholar
  4. 4.
    Aharonov, D., Elias, U.: Univalence criteria depending on parameters and applications. Contemp. Math. 667, 15–26 (2016)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Aliaga, E., Tuneski, N.: On existence of sufficient condition for univalence depending on two parameters. In: Proceedings of the V Congress of Mathematicians of Macedonia, vol. 2, pp. 5–9 (2015)Google Scholar
  6. 6.
    Aliaga, E., Tuneski, N.: The Schwarzian derivative as a condition for univalence. Adv. Math. Sci. J. 5, 111–116 (2016)MATHGoogle Scholar
  7. 7.
    Nehari, Z.: The Schwarzian derivative and schlicht functions. Bull. Am. Math. Soc. 55, 545–551 (1949)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Nehari, Z.: Some criteria of univalence. Proc. Am. Math. Soc. 5, 700–704 (1954)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Nehari, Z.: Univalence criteria depending on the Schwarzian derivative. Ill. J. Math. 23, 345–351 (1979)MathSciNetMATHGoogle Scholar
  10. 10.
    Tuneski, N., Jolevska-Tuneska, B., Prangoski, B.: On existence of sharp univalence criterion using the Schwarzian derivative. C. R. Acad. Bulg. Sci. 68, 569–576 (2015)MathSciNetMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.TechnionHaifaIsrael

Personalised recommendations