Israel Journal of Mathematics

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

Typically real mean univalent functions of large growth

  • B. G. Eke


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=+∞.


Riemann Surface Univalent Function Maximal Growth Conformal Mapping Large Growth 
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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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