Some generalizations of the class of functions convex in one direction
- 作者: Sevodin M.1
-
隶属关系:
- Perm National Research Polytechnic University
- 期: 卷 38, 编号 2 (2017)
- 页面: 364-370
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199104
- DOI: https://doi.org/10.1134/S1995080217020196
- ID: 199104
如何引用文章
详细
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.
作者简介
M. Sevodin
Perm National Research Polytechnic University
编辑信件的主要联系方式.
Email: m.sevodin@mail.ru
俄罗斯联邦, Komsomol’skii pr. 29, Perm, 614039