中文摘要：

对任意给定的α∈[0,1）,对单位圆盘D上规范化的保向调和映照类H的一个近于凸子类P^0（α）={f=h＋g∈H：R{h′（z）-α}〉｜g′（z）｜,z∈D,g′（0）=0}的性质进行了研究,如P-0（α）类的凸像和星象半径估计、偏差定理、像域面积的估计、拟共形性,其中得到的凸像和星象半径估计值改进了文献[8-9]中相应结果.此外,对包含P-0（α）的稳定单叶调和映照类（SHU）的Pre-Schwarz导数进行了考虑,得到了精确的上界估计.

英文摘要：

In this paper, the following subclass of H P^0（α）={f=h＋g∈H：R{h′（z）-α}〉｜g′（z）｜,z∈D,g′（0）=0} is studied, where α ∈ [0, 1） and H is the class of all normalized sense preserving harmonic mappings defined in the unit disk D. Estimations of the convexity and starlike radii of p^0（α） are given, which improve the relative results in [8, 9]. A distortion theorem and a lower bound of ｜f（D）｜ for all f ∈P^0（α） are obtained. The upper bound of Pre-Schwarzian norms of functions in a subclass of SHU containing P^0（α） is estimated and the quasiconformality is discussed also.