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

Authors: LEOPOLD KOCZAN, PAWEL ZAPRAWA

Abstract: We consider the class T(r) of typically real functions with the normalization f(0)=0 and f(r)=r for a fixed r \in (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 \bigcap_{f\in T(r)} f(\Delta). 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.

Keywords: Typically real functions, Koebe domain, Montel's normalization

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