International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 4, Pages 641-647

On holomorphic functions with certain extremal properties of its absolute values

Dieter Schmersau

Mathematisches Institut der Freien Universität Berlin, FB 19, WE 1, Hüttenweg 9, Berlin 33 1000, Germany

Received 4 March 1981

Copyright © 1981 Dieter Schmersau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with a special class of holomorphic functions with extremal properties of its absolute values on arbitrary closed line segments in the complex plane. The main result is a geometrical characterization of the functions zeaz+b, z(az+b)n and z(az+b)α+iβ with a,b,, α,β, n.