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Israel Journal of Mathematics

, Volume 22, Issue 1, pp 1–6 | Cite as

Typically real mean univalent functions of large growth

  • B. G. Eke
Article
  • 36 Downloads

Abstract

Typically real normalized κ-dimensionally mean univalent functionsf on |z|<1 are considered for which
$$\mathop {\lim \sup }\limits_{r \uparrow 1} \{ (1 - r)^2 \mathop {\max }\limits_{0 \leqslant \theta \leqslant 2\pi } \left| {f(re^{i\theta } )} \right|\} > 0$$
. Lets=logf(z) forz in the unit disc cut along (−1, 0]. A theorem is proved concerning the area of the Riemann surface over thes-plane which distinguishes the two cases −1≦κ<+∞ and κ=+∞.

Keywords

Riemann Surface Univalent Function Maximal Growth Conformal Mapping Large Growth 
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.

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References

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    James A. Jenkins and Kôtaro Oikawa,A remark on p-valent functions, J. Austral. Math. Soc.12 (1971), 397–404.MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    B. G. Eke,The asymptotic behaviour of a really mean valent functions, J. Analyse Math.20 (1967), 147–212.MATHMathSciNetGoogle Scholar
  3. 3.
    W. K. Hayman,Multivalent Functions, Cambridge, 1958.Google Scholar
  4. 4.
    S. E. Warschawski,On conformal mapping of infinite strips, Trans. Amer. Math. Soc.51 (1942), 280–335.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© The Weizmann Science Press of Israel 1975

Authors and Affiliations

  • B. G. Eke
    • 1
  1. 1.Department of Pure MathematicsThe University of SheffieldEngland

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