特定域上推广的Roper-Suffridge算子的性质

Property of the Generalized Roper-Suffridge Extension Operator on Specific Domains

讨论复Banach空间特定域上推广的Roper-Suffridge算子保持双全纯映照子族的性质,从定义出发证明推广后的算子在复Banach空间特定域上保持强β型螺形性及强α次殆星形性,进而得出推广后的算子在复Banach空间特定域上保持强星形性.所得结论为由复平面C中单位圆盘D上的强β型螺形映照、强α次殆星形映照及强星形映照来构造复Banach空间特定域上相应的映照提供了一种新的途径,从而对复Banach空间特定域上推广的Roper-Suffridge算子有了更进一步的认识.

In this paper, the authors discuss the property that the generalized Roper-Suffridge extension operator preserve subclasses of biholomorphic mappings on specific domains in complex Banach spaces. From the definition, they prove the fact that the generalized operator keeps strongly spirallikeness of typeβ and strong and almost starlikeness of order a on specific domains in complex Banach spaces, and then obtain that the generalized operator keeps strongly starlikeness on specific domains in complex Banach spaces. The conclusion provides a new approach for constructing corresponding mappings on specific domains in complex Banach spaces from strongly spirallike mappings of type/3, strong and almost starlike mappings of order a and strongly starlike mappings on the unit ball D in the complex plane Cn thus we have further understanding of the generalized Roper-Suffridge extension operator on specific domains in complex Banach spaces.