- Tytuł:
- Subclasses of typically real functions determined by some modular inequalities
- Autorzy:
-
Koczan, Leopold
Trąbka-Więcław, Katarzyna - Powiązania:
- https://bibliotekanauki.pl/articles/747067.pdf
- Data publikacji:
- 2010
- Wydawca:
- Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
- Tematy:
-
Typically real functions
majorization
subordination - Opis:
- Let \(\mathrm{T}\) be the family of all typically real functions, i.e. functions that are analytic in the unit disk \(\Delta := \{ z \in \mathbb{C} : |z|<1 \}\), normalized by \(f(0)=f'(0)-1=0\) and such that Im \(z\) Im \(f(z)\) \(\geq 0\) for \(z \in \Delta\). Moreover, let us denote: \(\mathrm{T}^{(2)}:= \{f \in \mathrm{T}: f(z)=-f(-z) \text{ for } z \in \Delta \}\) and \(\mathrm{T}^{M,g} := \{ f \in \mathrm{T}: f \prec Mg \text{ in } \Delta \}\), where \(M>1\), \(g \in \mathrm{T} \cap \mathrm{S}\) and \(\mathrm{S}\) consists of all analytic functions, normalized and univalent in \(\Delta\).We investigate classes in which the subordination is replaced with the majorization and the function \(g\) is typically real but does not necessarily univalent, i.e. classes \(\{ f \in \mathrm{T}: f \ll Mg \text{ in } \Delta \}\), where \(M>1\), \(g \in \mathrm{T}\), which we denote by \(\mathrm{T}_{M,g}\). Furthermore, we broaden the class \(\mathrm{T}_{M,g}\) for the case \(M \in (0,1)\) in the following way:\(\mathrm{T}_{M,g} = \left\{ f \in \mathrm{T} : |f(z)| \geq M |g(z)| \text{ for } z \in \Delta \right\}\), \(g \in \mathrm{T}\).
- Źródło:
-
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2010, 54, 1
0365-1029
2083-7402 - Pojawia się w:
- Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł