B^n上螺形映照的子族与推广的Roper-Suffridge算子

Subclasses of Spiral-like Mappings on B^n and the Generalized Roper-Suffridge Extension Operators

讨论在C^n中单位球B^n上强α次殆β型螺形映照在一些推广的Roper-Suffridge算子下的不变性.从定义出发,利用双全纯映照的偏差结论证明推广后的Roper-Suffridge算子在一定的条件下保持强α次殆β型螺形性,从而得到推广后的算子保持强β型螺形性、强α次殆星形性及强星形性.

In this paper,the authors discuss the invariance of strong and almost spiral-like mappingns of type β and order α under some generallized Roper-Suffridge extension operators on the unit ball B^n in C^n.From the definitions and the distortion theorems of biholomorphic mappings,they prove that the generallized operators keep strong and almost spirallikeness of type β and order α,thus they obtain that the generallized operators keep strong spirallikeness of type β,strong and almost starlikeness of order α as well as strong starlikeness.