Geometric Mappings under the Perturbed Extension Operators in Complex Systems Analysis

In this paper, we mainly seek conditions on which the geometric properties of subclasses of biholomorphic mappings remain unchanged under the perturbed Roper-Suffridge extension operators. Firstly we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Secondly, applying the analytical characteristics and growth results of subclasses of biholomorphic mappings, we conclude that the generalized Roper-Suffridge operators preserve the geometric properties of strong and almost spiral-like mappings of type beta and order alpha,S-Omega(*) (beta,A,B) as well as almost spiral-like mappings of type beta and order alpha under different conditions on Bergman-Hartogs domains. Sequentially we obtain the conclusions on the unit ball B-n and for some special cases. The conclusions include and promote some known results and provide new approaches to construct biholomorphic mappings which have special geometric characteristics in several complex variables.