Let be the class of functions analytic and univalent in . In this paper we investigate the problem to maximize in two subclasses of : (i) the class of all functions which omit two given values and (ii) the class of all functions with which map onto regions of prescribed width in the direction of the imaginary axis. We solve these problems by applying a variational method to a coefficient problem in two subclasses of univalent Bieberbach-Eilenberg functions which are equivalent to these problems.
Cite this article
Siegfried Kirsch, Univalent Functions with Range Restrictions. Z. Anal. Anwend. 19 (2000), no. 4, pp. 1057–1073DOI 10.4171/ZAA/998