Skip to main content
SpringerLink
Log in

Univalence criteria depending on parameters

  • Published:
Analysis and Mathematical Physics Aims and scope Submit manuscript

Abstract

The article discusses criteria for univalence of analytic functions in the unit disc. A unified method for creating new sets of conditions ensuring univalence is presented. Applying this method we are able to find several families of new sharp criteria for univalence.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aharonov, D., Elias, U.: Singular Sturm comparison theorems. J. Math. Anal. Appl. 371, 759–763 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aharonov, D., Elias, U.: More Jordan type inequalities. Math. Inequ. Appl. (preprint)

  3. Beesack, P.R.: Nonoscillation and disconjugacy in the complex domain. Trans. Am. Math. Soc. 81, 211–242 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chuaqui, M., Duren, P., Osgood, B., Stowe, D.: Oscillation of solutions of linear differential equations. Bull. Aust. Math. Soc. 79, 161–169 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hille, E.: Remarks on a paper by Zeev Nehari. Bull. Am. Math. Soc. 55, 552–553 (1949)

    Article  MATH  MathSciNet  Google Scholar 

  6. Nehari, Z.: The Schwarzian derivative and schlicht functions. Bull. Am. Math. Soc. 55, 545–551 (1949)

    Article  MATH  MathSciNet  Google Scholar 

  7. Nehari, Z.: Some criteria of univalence. Proc. Am. Math. Soc. 5, 700–704 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  8. Nehari, Z.: Univalence criteria depending on the Schwarzian derivative. Illinois J. Math. 23, 345–351 (1979)

    MATH  MathSciNet  Google Scholar 

  9. Pokornyi, V.V.: On some sufficient conditions for univalence. Dokl. Akad. Nauk SSSR 79, 743–746 (1951)

    MathSciNet  Google Scholar 

  10. Spanier, J., Oldham, K.B.: An Atlas of Functions. Hemisphere Publishing Corporation, New York (1987)

    MATH  Google Scholar 

  11. Steinmetz, N.: Homeomorphic extensions of univalent functions. Complex Var. 6, 1–9 (1986)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    D. Aharonov & U. Elias

Authors
  1. D. Aharonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. U. Elias
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to U. Elias.

Additional information

Dedicated to Larry Zalcman on the occasion of his 70-th birthday.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aharonov, D., Elias, U. Univalence criteria depending on parameters. Anal.Math.Phys. 4, 23–34 (2014). https://doi.org/10.1007/s13324-014-0076-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13324-014-0076-y

Keywords

Search

Navigation