摘要
定义了螺形函数的新子族,即ρ次椭圆星形函数和ρ次椭圆形β型螺形函数,并将这些定义推广到多复变数空间中,得到推广的Roper-Suffridge算子在不同空间不同区域上保持ρ次椭圆星形映照和ρ次椭圆形β型螺形映照的性质,由此可以在多复变数空间中构造出许多ρ次椭圆形β型螺形映照.所得结论丰富了对螺形映照子族及推广的Roper-Suffridge算子的研究.
In this paper,we introduce some new subclasses of spirallike functions,namely elliptical starlike functions of order ρ,elliptical and spirallike functions of type β and orderρ.We extend the new definitions and obtain that the generalized Roper-Suffridge operators preserve the properties of the mappings defined in this paper on different domains in different spaces,thus many elliptical and spirallike mappings of type β and order ρ can be constructed in several complex variables.The conclusions enrich the research of subclasses of spirallike mappings and generalized Roper-Suffridge operators.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2015年第4期683-694,共12页
Acta Mathematica Scientia
基金
国家自然科学基金(11271359
U1204618)
河南省自然科学基金(2011B110034)
河南省教育厅科学技术研究重点项目(14B110015
14B110016)资助
