A Simple Proof of the Lower Bounds of Distortion Theorems on the Roper-Suffridge Operator

In this paper,we prove that the generalized Roper-Suffridge extension operator can be embedded in Loewner chains on the unit ball in Hibert spaces,and obtain the fact that the operator keeps the properties of almost spirallike mapping of type β and other α,almost starlikeness of order α,spirallikeness of type β and starlikeness.

The Study for Some Subclasses of Biholomorphic Mappings by an Unified Method

让 Cn 是有 0 的一个围住的星形的圆形的领域。在这份报纸，我们上介绍 holomorphic mappings Mg 的一个班。让 f (z) 一局部地使 biholomorphic 印射在上正常化以便 J-1f (z) f (z) Mg 和 z=0 是 f (z) 的零顺序 k+1 - z。我们为 f (z) 获得生长和盖住的定理。作为推论，特别，我们统一并且概括许多已知的结果。而且鉴于推论的证明，在星形的 mappings 的子类之中的必要关系被显示出。