改进的Roper-Suffridge算子的性质及其偏差

The Property and the Distortion of the Generalized Roper-Suffridge Extension Operators

进一步推广了Roper-Suffridge算子,并讨论推广后的算子保持双全纯映照子族的一些性质,从定义出发证明推广后的算子在G^n中的单位球B^n上保持α次β型螺形性及强β型螺形性,并作为特殊情况得出推广后的算子在相应域上保持α次星形性及强星形性,且讨论了推广后的Roper-Suffridge算子的偏差定理.

In this paper, the authors generalize the Roper-Suffridge extension operator, and discuss that the generalized operators preserve some properties of subclasses of biholomorphic mappings. From the definition, they prove the fact that the generalized operators preserve spirallikeness of type β and order α and strongly spirallikeness of type β, and as the special case, they obtain that the generalized operators preserve starllikeness of order α and strongly starllikeness on the corresponding domain, and they also research the distortion of the generalized operators.