Abstract
In this article, we extend the well-known Roper-Suffridge operator on Bn+1 and bounded complete Reinhardt domains in ℂn+1, then we investigate the properties of the generalized operators. Applying the Loewner theory, we obtain the mappings constructed by the generalized operators that have parametric representation on Bn+1. In addition, by using the geometric characteristics and the parametric representation of subclasses of spirallike mappings, we conclude that the extended operators preserve the geometric properties of several subclasses of spirallike mappings on Bn+1 and bounded complete Reinhardt domains in ℂn+1. The conclusions provide new approaches to construct mappings with special geometric properties in ℂn+1.
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