复Banach空间上推广的Roper-Suffridge算子

从定义出发证明复Banach空间特定域上推广的Roper-Suffridge算子保持α次强β型螺形性及ρ次抛物型β型螺形性,由此得到推广后的算子在复Banach空间特定域上保持α次强星形性、ρ次抛物星形性及抛物星形性,为由复平面C中单位圆盘D上的α次强β型螺形映照及ρ次抛物β型螺形映照来构造复Banach空间特定域上相应的映照提供了一种新的途径,充实了对Roper-Suffridge算子的研究.

Generalized Roper-Suffridge Extension Operators in Complex Banach Spaces

In this paper,with the definition the authors prove the fact that the generalized Roper-Suffridge extension operators keep strongly spirallikeness of type β and order α and parabolic and spiralikeness of type β and order pon specific domains in a complex banach space,thus they obtain that the extended operators keep strongly starlikeness of order αparabolic and starlikeness of order pand parabolic and starlikeness on specific domains in a complex banach space.Ths paper provides a new approach for constructing corresponding mappings on specific domains in a complex Banach space from strongly spirallike mappings of type β and order α and parabolic and spiralike mappings of type β and order ρon the unit ball D in the complex plane C,and it alao enriches the study of the generallized Roper-Suffridge extension operator.