Some generalizations of the class of functions convex in one direction
- Autores: Sevodin M.1
-
Afiliações:
- Perm National Research Polytechnic University
- Edição: Volume 38, Nº 2 (2017)
- Páginas: 364-370
- Seção: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199104
- DOI: https://doi.org/10.1134/S1995080217020196
- ID: 199104
Citar
Resumo
This paper concerns the extension of univalent conditions known for a ring domain to the case of a half-plane. We study the possibilities of applying Rahman and Brickman methods to functions analytic in the upper half-plane. Some generalizations of the functions convex in one direction are obtained. We also investigate the curvelinear half-planes, the boundary of which can be attained by a family of shift curves, and demonstrate the efficiency of the quasiconformal extension method. The subclasses of domains, whose boundaries are quasiconformal curves, are identified. Some sufficient conditions for univalence of functions analytic in these domains are established.
Palavras-chave
Sobre autores
M. Sevodin
Perm National Research Polytechnic University
Autor responsável pela correspondência
Email: m.sevodin@mail.ru
Rússia, Komsomol’skii pr. 29, Perm, 614039