Turkish Journal of Mathematics
DOI
10.3906/mat-1304-55
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
First Page
246
Last Page
251
Recommended Citation
KOCZAN, LEOPOLD and ZAPRAWA, PAWEL
(2014)
"The new method of determining Koebe domains for the class of typically real functions under Montel's normalization,"
Turkish Journal of Mathematics: Vol. 38:
No.
2, Article 7.
https://doi.org/10.3906/mat-1304-55
Available at:
https://journals.tubitak.gov.tr/math/vol38/iss2/7
