In this article, we extend the well-known Roper-Suffridge operator on $B^{n+1}$ and bounded complete Reinhardt domains in $\mathbb{C}^{n+1}$, 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 $B^{n+1}$. 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 $B^{n+1}$ and bounded complete Reinhardt domains in $\mathbb{C}^{n+1}$. The conclusions provide new approaches to construct mappings with special geometric properties in $\mathbb{C}^{n+1}$.
Yanyan CUI
,
Chaojun WANG
,
Hao LIU
. THE EXTENSION OPERATORS ON Bn+1 AND BOUNDED COMPLETE REINHARDT DOMAINS[J]. Acta mathematica scientia, Series B, 2020
, 40(5)
: 1271
-1288
.
DOI: 10.1007/s10473-020-0508-8
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