- Turkish Journal of Mathematics
- Vol: 38 Issue: 2
- The new method of determining Koebe domains for the class of typically real functions under Montel's...
The new method of determining Koebe domains for the class of typically real functions under Montel's normalization
Authors : Leopold Koczan, Pawel Zaprawa
Pages : 246-251
Doi:10.3906/mat-1304-55
View : 13 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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 \bigcapf\in T(r) f(D). 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