| In this paper,the definition of the starlike mappings of complex order on the unit disk is extended to the high-dimensional complex space,and the properties of the homogeneous expansion coefficient of the mapping belonging to the subclass of biholomorphic mappings are discussed under the background of several complex variables.The main research contents are divided into two aspects:(1)The common solutions of Fekete-Szeg(?) problem of elevating version in the finite dimensional complex Banach sapce unit ball,high-dimensional complex Euclidean space unit polydisc and bounded starlike circular domain are given,and the extreme mappings are verified.(2)The bounds of all coefficient estimates of homogeneous expansion are obtained when the subclass ofg-parametric biholomorphic mappings on the ball of finite dimensional complex Banach space and the unit polydisc of high-dimensional complex Euclidean sapce satisfy certain conditions.Compared with the previous results,we get better results without some strong restrictive conditions,and the proof method is relatively simple.The main content of the research enriches the form of associated Bieberbach conjecture in the field of geometric function theory of several complex variables. |
