On semi-typically real functions

• Autorzy: Leopold Koczan , Katarzyna Trąbka-Więcław
• Języki publikacji: EN

Abstrakty

EN

Suppose that A is the family of all functions that are analytic in the unit disk Δ and normalized by the condition [...] For a given A ⊂ A let us consider the following classes (subclasses of A): [...] and [...] where [...] and S consists of all univalent members of A.In this paper we investigate the case A = τ, where τ denotes the class of all semi-typically real functions, i.e. [...] We study relations between these classes. Furthermore, we find for them sets of variability of initial coeffcients, the sets of local univalence and the sets of typical reality.

Słowa kluczowe

EN

Typically real functions; sets of variability of coeffcients

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2009
• Tom: 63
• Numer: 1
• Strony: 139-148

Daty

wydano

2009-01-01

online

2010-01-22

Twórcy

autor

Leopold Koczan

• Department of Applied Mathematics, Lublin University of Technology, ul. Nadbystrzycka 38D, 20-618 Lublin, Poland

autor

Katarzyna Trąbka-Więcław

• Department of Applied Mathematics, Lublin University of Technology, ul. Nadbystrzycka 38D, 20-618 Lublin, Poland

Bibliografia

• Duren, P. L., Univalent Functions, Springer-Verlag, New York, 1983.
• Goluzin, G. M., On typically real functions, Mat. Sb. 27(69) (1950), 201-218 (Russian).
• Goodman, A. W., Univalent Functions, Mariner Publ. Co., Tampa, 1983.
• Koczan, L., On classes generated by bounded functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 52, no. 2 (1998), 95-101.
• Koczan, L., Szapiel, W., Extremal problems in some classes of measures. IV. Typically real functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 43 (1989), 55-68 (1991).
• Koczan, L., Zaprawa, P., Koebe domains for the classes of functions with ranges included in given sets, J. Appl. Anal. 14, no. 1 (2008), 43-52.
• Koczan, L., Zaprawa, P., On typically real functions with n-fold symmetry, Ann. Univ. Mariae Curie-Skłodowska Sect. A 52, no. 2 (1998), 103-112.
• Zaprawa, P., On typically real bounded functions with n-fold symmetry, Folia Scientiarum Universitatis Technicae Resoviensis, Mathematics 21, no. 162 (1997), 151-160.

Identyfikatory

DOI

10.2478/v10062-009-0013-y