Subclasses of Biholomorphic Mappings Under the Extension Operators

In this article, we mainly study the invariance of some biholomorphic mappings with special geometric characteristics under the extension operators. First we generalize the Roper-Suffridge extension operators on Bergman-Hartogs domains. Then, by the geometric characteristics of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve the properties of SΩ* (β,A,B), parabolic and spirallike mappings of type β and order ρ, strong and almost spirallike mappings of type β and order α as well as almost starlike mappings of complex order λ on \(\Omega_{p_{1}}^{B^{n}},\ldots,_{p_{s},q}\) under different conditions, respectively. The conclusions provide new approaches to construct these biholomorphic mappings in several complex variables.