Koebe domains for certain families

Certain Conditions for Starlikeness of Analytic Functions of Koebe Type

For α ≥ 0, λ > 0, we consider theM α, λ b of normalized analytic α−λ convex functions defined in the open unit disc U. In this paper, we investigate the classM α, λ b, that is, Re{ zf ′ b z /fb z 1− α α 1 − λ zf ′ b z /fb z αλ 1 zf ′′ b z /f ′ b z } > 0, with fb is Koebe type, that is, fb z : z/ 1−zn . The subordination result for the aforementioned class will be given. Further, bymaking use of...

Feigenbaum Numbers for Certain Flat-Top Families

We report on numerical results for certain families of S-unimodal maps with flat critical point. For four one-parameter families, differing in their amount of flatness, we study the Feigenbaum-limits α and δ. There seems to be a finite δ and a finite α associated with each period doubling cascade in each family. Some rough numerical estimates are obtained. One would expect that these numbers sh...

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.

Szegö Kernels for Certain Unbounded Domains

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...