Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1304-55
Keywords
Typically real functions, Koebe domain, Montel's normalization
First Page
246
Last Page
251
Recommended Citation
KOCZAN, L, & ZAPRAWA, P (2014). The new method of determining Koebe domains for the class of typically real functions under Montel's normalization. Turkish Journal of Mathematics 38 (2): 246-251. https://doi.org/10.3906/mat-1304-55
