The new method of determining Koebe domains for the class of typically real functions under Montel’s normalization

We consider the class T (r) of typically real functions with the normalization f (0) = 0 and f (r) = r for a fixed r ∈ (0, 1) . In the limiting case, when r tends to 0, the class T (r) coincides with the class T of typically real functions normalized by f (0) = f (0) − 1 = 0 . In 1980, Lewandowski and Miazga determined the Koebe domain for T (r) , i.e. the set of the form ∩ f ∈T(r) f (∆) . They used the method applied earlier by Goodman. In this paper we present a new, complete method of determining this set. As a corollary, we obtain the Koebe set for T.