Real C Koebe Principle

Koebe Domains for the Classes of Functions with Ranges Included in given Sets

In this paper we present a new method of determining Koebe domains. We apply this method by giving a new proof of the well-known theorem of A. W. Goodman concerning the Koebe domain for the class T of typically real functions. We applied also the method to determine Koebe sets for classes of the special type, i.e. for T = {f ∈ T : f(∆) ⊂ Mg(∆)}, g ∈ T ∩ S, M > 1, where ∆ = {z ∈ C : |z| < 1} and...

Dynamics of Certain Smooth One-dimensional Mappings I. The C-Denjoy-Koebe distortion lemma

We prove a technical lemma, the C-Denjoy-Koebe distortion lemma, estimating the distortion of a long composition of a C onedimensional mapping f : M 7→ M with finitely many, non-recurrent, power law critical points. The proof of this lemma combines the ideas of the distortion lemmas of Denjoy and Koebe.

Covering problems for functions n-fold symmetric and convex in the direction of the real axis

Let F denote the class of all functions univalent in the unit disk and convex in the direction of the real axis. In the paper we discuss the functions of the class F which are n-fold symmetric, where n is positive even integer. For the class of such functions we find the Koebe set as well as the covering set, i.e. T f2F f ðDÞ and S f2F f ðDÞ. Moreover, the Koebe constant and the covering consta...

The starlikeness of analytic functions of Koebe type

We investigate the new class H b (α, β) of analytic functions with Koebe type. The subordination, superordination, best dominant result for that class was obtain. And by making use of Jack's Lemma as well as several differential and other inequalities, the authors derive sufficient conditions for starlikeness of the class H b (α, β) of n-fold symmetric analytic functions of Koebe type. Relevant...

Note on a Theorem of Bôcher and Koebe*