Koebe sets for certain classes of circularly symmetric functions
Artykuł w czasopiśmie
MNiSW
20
Lista A
| Status: | |
| Autorzy: | Zaprawa Paweł |
| Rok wydania: | 2016 |
| Wersja dokumentu: | Drukowana | Elektroniczna |
| Język: | angielski |
| Numer czasopisma: | 3 |
| Wolumen/Tom: | 354 |
| Strony: | 245 - 252 |
| Web of Science® Times Cited: | 0 |
| Scopus® Cytowania: | 0 |
| Bazy: | Web of Science | Scopus | Web of Science Core Collection | Zentralblatt MATH | Mathematical Reviews | Expanded |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | NIE |
| Abstrakty: | angielski |
| A function f analytic in Δ≡{ζ∈C:|ζ|<1}, normalized by f(0)=f′(0)−1=0, is said to be circularly symmetric if the intersection of the set f(Δ) and a circle {ζ∈C:|ζ|=ϱ} has one of three forms: the empty set, the whole circle, an arc of the circle which is symmetric with respect to the real axis and contains ϱ. By X we denote the class of all circularly symmetric functions, and by Y the subclass of X consisting of univalent functions. The main concern of the paper is to determine two Koebe sets: for the class Y∩K(i) of circularly symmetric functions that are convex in the direction of the imaginary axis and for the class Y∩S⁎ of circularly symmetric and starlike functions, i.e. sets of the form KY∩K(i)=⋂f∈Y∩K(i)f(Δ) and KY∩S⁎=⋂f∈Y∩S⁎f(Δ). In the last section of the paper, we consider a similar problem for the class Y∩S⁎∩K(i). |
