Skip to main content
SpringerLink
Log in

Estimates on integral means of the derivatives of univalent functions

  • Published:
Journal d’Analyse Mathématique Aims and scope

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

References

  1. A. Baernstein II,Integral means, univalent functions, and circular symmetrization, Acta Math.133 (1974), 139–169.

    Article  MathSciNet  Google Scholar 

  2. L. Brickman, T. H. MacGregor and D. R. Wilken,Convex hulls of some classical families of univalent functions, Trans. Amer. Math. Soc.,156 (1971), 91–107.

    Article  MATH  MathSciNet  Google Scholar 

  3. C. Caratheodory,Theory of Functions, Vol. 2, Chelsea, New York, 1954.

    Google Scholar 

  4. J. Clunie and F. R. Keogh,On starlike and convex schlicht functions, J. London Math. Soc.,35, (1960), 229–233.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Clunie and P. L. Duren,Addendum: an arclength problem for close-to-convex functions. J. London Math. Soc.41 (1966), 181–182.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. J. Eenigenburg and F. R. Keogh,The Hardy class of some univalent functions and their derivatives, Michigan Math. J.17 (1970), 335–346.

    Article  MATH  MathSciNet  Google Scholar 

  7. Jinfu Feng and T. H. MacGregor,Integral mean estimates for derivatives of functions with a positive real part (to appear).

  8. G. M. Golusin,Geometric Theory of Functions of a Complex Variable, American Mathematical Society, Providence, 1969.

    Google Scholar 

  9. D. J. Hallenbeck,Some inequalities for convex, starlike, and close-to-convex mappings, Czechoslovak Math. J.24 (99) (1974), 411–415.

    MathSciNet  Google Scholar 

  10. W. K. Hayman,Multivalent Functions, Cambridge University Press, Cambridge, 1967.

    Google Scholar 

  11. W. Kaplan,Close to convex schlicht functions, Michigan Math. J.1 (1952), 169–185.

    Article  MATH  MathSciNet  Google Scholar 

  12. E. Landau,Einige Bemerkungen über schlichte Abbildung, Jber. Deutsche Math.-Verein34 (1926), 239–243.

    Google Scholar 

  13. J. E. Littlewood,Lectures on the Theory of Functions, Oxford University Press, Oxford, 1944.

    MATH  Google Scholar 

  14. A. J. Lohwater, G. Piranian and W. Rudin,The derivative of a schlicht function, Math. Scand.3 (1955), 103–106.

    MATH  MathSciNet  Google Scholar 

  15. T. H. MacGregor,Applications of extreme-point theory to univalent functions, Michigan Math. J.19 (1972), 361–376.

    Article  MATH  MathSciNet  Google Scholar 

  16. T. H. MacGregor,Rotations of the range of an analytic function, Math. Ann.201 (1973), 113–126.

    Article  MATH  MathSciNet  Google Scholar 

  17. A. Marx,Untersuchungen über schlichte Abbildungen, Math. Ann.107, (1932), 40–67.

    Article  MATH  MathSciNet  Google Scholar 

  18. Ch. Pommerenke,On the coefficients of close-to-convex functions, Michigan Math. J.9 (1962), 259–269.

    Article  MATH  MathSciNet  Google Scholar 

  19. Ch. Pommerenke,Linear-invariant Familien analytischer Functionen I, Math. Ann.155 (1964), 108–154.

    Article  MATH  MathSciNet  Google Scholar 

  20. Ch. Pommerenke,Lacunary power series and univalent functions, Michigan Math. J.11 (1964), 219–223.

    Article  MATH  MathSciNet  Google Scholar 

  21. Ch. Pommerenke,Problems in complex function theory, Bull. London Math. Soc.4 (1972), 354–366.

    Article  MATH  MathSciNet  Google Scholar 

  22. M. S. Robertson,On the theory of univalent functions, Ann. of Math., (2)37 (1936), 374–408.

    Article  MathSciNet  Google Scholar 

  23. E. Strohhäcker,Beiträge zur Theorie der schlichten Funktionen, Math. Z.37 (1933), 356–380.

    Article  MATH  MathSciNet  Google Scholar 

  24. D. R. Wilken,The integral means of close-to-convex functions, Michigan Math. J.,19 (1972), 377–379.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State University of New York, Albany, New York

    Jinfu Feng & Thomas H. Macgregor

  2. University of Maryland, College Park, Maryland

    Jinfu Feng & Thomas H. Macgregor

Authors
  1. Jinfu Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas H. Macgregor
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Most of the results in this paper are contained in the first author’s Ph.D. dissertation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feng, J., Macgregor, T.H. Estimates on integral means of the derivatives of univalent functions. J. Anal. Math. 29, 203–231 (1976). https://doi.org/10.1007/BF02789979

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02789979

Keywords

Search

Navigation