On Univalent Functions with Two Preassigned Values

Abstract

Let 311« denote the class of functions analytic and univalent in the unit disc A subject to the conditionswhere 2o, zo^O, is a fixed point of A and 1 =.W= <».In the present note, we determine by the method of circular symmetrization, the exact value of the "Koebe constant" for the class 9TC¿f.We also determine Koebe sets for the class 91t¿f consisting of the starlike functions, and for 9Tt£f, consisting of all functions mapping A onto domains convex in the direction e'a.

Locations

• Proceedings of the American Mathematical Society - View - PDF