沿单位方向上的ρ次抛物星形映射的偏差定理

The Distortion Theorem for Parabolic Starlike Mappings of Order p Along Unit Direction

目前多种双全纯映射的偏差估计结果还较少.针对这一情况,本文研究了复Banach空间中开单位球B及欧氏空间中单位多圆柱D_n单位方向上的p次抛物星形映射的偏差估计问题.利用ρ次抛物星形映射定义中的不等式及已知的增长结果,获得了上述域上的ρ次抛物星形映射的偏差估计.

There have been few distortion results about various types of biholomorphic mappings. Aiming to this issue, the paper studies the distortion estimation of parabolic starlike mappings of order p along unit direction on unit ball B in complex Banach space and unit polydisc Dn in Euclidean space. By using the inequalities appeared in the definition of the parabolic starlike mapping of order p and the known growth result, we obtain the distortion estimation on the above several domains.