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
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 , and with , , .