Journal of Mathematical Sciences

, Volume 83, Issue 6, pp 745–749 | Cite as

The value regions of initial coefficients in a certain class of meromorphic functions

  • E. G. Goluzina


Let Mk,λ(0≤λ≤1, k≥2) be the class of functions f(z)=1/z+ao+a1z+... that are regular and locally univalent for 0<⩛z⩛<1 and satisfy the condition\(\mathop {\lim }\limits_{r \to 1 - } \int\limits_0^{2\pi } {\left| {\operatorname{Re} J_\lambda \left( {re^{i\theta } } \right)} \right|} d\theta \leqslant k\pi ,\) where Jλ(z)=λ(1+zf″(z)/f'(z))+(1-λ)zf'(z)/f(z). In the class Mk,λ we consider sorne coefficient problems and problems concerning distortion theorems.


Meromorphic Function Univalent Function Regular Function Real Coefficient Michigan Math 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    E. G. Goluzina, “On the value regions of the initial coefficients in the class of meromorphic functions with bounded boundary rotation,”Zap. Nauchn. Semin. LOMI,168, 23–31 (1988).Google Scholar
  2. 2.
    J. Pfaltzgraff and B. Pinchuk, “A variational method for classes of meromorphic functions,”J. Anal. Math.,24, 101–150 (1971).MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    J. Noonan, “Meromorphic functions of bounded boundary rotation,”Michigan Math. J.,18, 343–352 (1971).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    E. G. Goluzina, “On the value regions of certain functionals on classes of regular functions,”Zap. Nauchn. Semin. LOMI,144, 46–50 (1985).MathSciNetMATHGoogle Scholar
  5. 5.
    E. G. Goluzina, “On the value regions of systems of functionals in certain classes of regular functions,”Mat. Zametki,37, 803–810 (1985).MathSciNetGoogle Scholar
  6. 6.
    E. G. Goluzina, “Some extremal problems in the class of functions with bounded boundary rotation of complex order”Zap. Nauchn. Semin. POMI,196, 35–40 (1991).MATHGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • E. G. Goluzina

There are no affiliations available

Personalised recommendations