- Tytuł:
- Estimations of the second coefficient of a univalent, bounded, symmetric and non-vanishing function by means of Loewners parametric method
- Autorzy:
- Śladkowska, J.
- Powiązania:
- https://bibliotekanauki.pl/articles/1294445.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
univalent function
Loewner differential equation - Opis:
- Let $₀^{(R)}(b)$ denote the class of functions F(z) = b + A₁z + A₂z² + ...$ analytic and univalent in the unit disk U which satisfy the conditions: F(U) ⊂ U, 0 ∉ F(U), $Im F^{(n)}(0) = 0$. Using Loewner's parametric method we obtain lower and upper bounds of A₂ in $₀^{(R)}(b)$ and functions for which these bounds are realized. The class $₀^{(R)}(b)$, introduced in [6], is a subclass of the class $_u$ of bounded, non-vanishing univalent functions in the unit disk. This last class and closely related ones have been studied by various authors in [1]-[4]. We mention in particular the paper of D. V. Prokhorov and J. Szynal [5], where a sharp upper bound for the second coefficient in $_u$ is given.
- Źródło:
-
Annales Polonici Mathematici; 1998, 68, 2; 119-123
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł