Second Order Differential Subordinations of Holomorphic Mappings on Bounded Convex Balanced Domains in $C^n$

摘要

In this paper, we obtain some second order differential subordinations of holomorphic mappings on a bounded convex balanced domain in . These results imply some first order differential subordinations of holomorphic mappings on a bounded convex balanced domain in . When is the unit disc in the complex plane , these results are just ones of Miller and Mocanu et al. about differential subordinations of analytic functions on the unit disc in the complex plane .