On the convex sum of certain univalent functions and the identity function
If g(z) is analytic, univalent, and convex in the unit disk E = {|z| and lt; 1}, g(0) = 0, g'(0) = 1, we extend some known results about the classification of Hλ(z) = λZ+ (1- λ)g(Z)when λ ≥ 0. In particular, it is proved Hλ is starlike in E for each λ ∈ [0, 1] when g" (0) = 0.
- Autores:
-
Merkes, E. P.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1987
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/42881
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/42881
http://bdigital.unal.edu.co/32979/
- Palabra clave:
- Analytic
univalent
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | If g(z) is analytic, univalent, and convex in the unit disk E = {|z| and lt; 1}, g(0) = 0, g'(0) = 1, we extend some known results about the classification of Hλ(z) = λZ+ (1- λ)g(Z)when λ ≥ 0. In particular, it is proved Hλ is starlike in E for each λ ∈ [0, 1] when g" (0) = 0. |
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