Koebe domains for the classes of functions with ranges included in given sets

• Autorzy: Koczan L. , Zaprawa P.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present a new method of determining Koebe domains. We apple 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^M,g = {∫ ∈ T : ∫(Δ) ⊂ Mg(Δ)}, g ∈ T ∩ S, M > 1, where Δ = {z ∈ C: IzI < 1} and T, S stand for the classes of tipically real functions and univalent functions respectively. In particular, we find the Koebe domains for the class T (M) of all typically real functions with ranges in a given strip.

Słowa kluczowe

EN

typically real functions; Koebe domain; subordination

PL

typowe funkcje rzeczywiste; podrzędność

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2008
• Tom: Vol. 14, nr 1
• Strony: 43--52
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Koczan L.

autor

Zaprawa P.

• Lublin University of Technology. department of applied Mathematics, Nadbystrzycka 38 D, 20-618 Poland,

Bibliografia

• [1] Golusin, G., On typically-real functions (Russian), Mat. Sb. 27(69) (1950), 201-218.
• [2] Goodman, A. W ., The domain covered by a typically real function, Proc. Amer. Math. Soc. 64 (1977), 233-237.
• [3] Koczan, L., On classes generated by bounded functions, Ann. Univ. Mariae Curie Sklodowska Sect. A 52(2) (1998), 95-10.
• [4] Koczan, L., Szapiel, W., Extremal problems in some classes of measure (IV): typically real functions, Ann. Univ. Mafiae Curie Sklodowska Sect. A 43 (1989), 55-68.
• [5] Rogosinski, W. W., Ueber positive harmonische Entwicklungen und tipisch-reelle Potenzreichen (German), Math. Z. 35 (1932), 93-121.