- Tytuł:
- Hyperbolically convex functions
- Autorzy:
-
Ma, Wancang
Minda, David - Powiązania:
- https://bibliotekanauki.pl/articles/1311659.pdf
- Data publikacji:
- 1994
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
hyperbolic convexity
distortion theorem
growth thoerem
linear invariance - Opis:
- We investigate univalent holomorphic functions f defined on the unit disk such that f() is a hyperbolically convex subset of ; there are a number of analogies with the classical theory of (euclidean) convex univalent functions. A subregion Ω of is called hyperbolically convex (relative to hyperbolic geometry on ) if for all points a,b in Ω the arc of the hyperbolic geodesic in connecting a and b (the arc of the circle joining a and b which is orthogonal to the unit circle) lies in Ω. We give several analytic characterizations of hyperbolically convex functions. These analytic results lead to a number of sharp consequences, including covering, growth and distortion theorems and the precise upper bound on |f''(0)| for normalized (f(0) = 0 and f'(0) > 0) hyperbolically convex functions. In addition, we find the radius of hyperbolic convexity for normalized univalent functions mapping into itself. Finally, we suggest an alternate definition of "hyperbolic linear invariance" for locally univalent functions f: → that parallels earlier definitions of euclidean and spherical linear invariance.
- Źródło:
-
Annales Polonici Mathematici; 1994-1995, 60, 1; 81-100
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł