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 .

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