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| New Subclasses of Biholomorphic Mappings and the ModifiedRoper-Suffridge Operator |
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Citation： |
Chaojun WANG,Yanyan CUI,Hao LIU.New Subclasses of Biholomorphic Mappings and the ModifiedRoper-Suffridge Operator[J].Chinese Annals of Mathematics B,2016,37(5):691~704 |
| Page view： 1330
Net amount： 1189 |
Authors： |
Chaojun WANG; Yanyan CUI;Hao LIU |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11271359, 11471098), the Joint Funds of
the National Natural Science Foundation of China (No.U1204618) and
the Science and Technology Research Projects of Henan Provincial
Education Department (Nos.14B110015, 14B110016). |
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| Abstract： |
The authors propose a new approach to construct subclasses of
biholomorphic mappings with special geometric properties in several
complex variables. The Roper-Suffridge operator on the unit ball
$B^{n}$ in $\mathbb{C}^{n}$ is modified. By the analytical
characteristics and the growth theorems of subclasses of spirallike
mappings, it is proved that the modified Roper-Suffridge operator
$[\Phi_{G, \gamma}(f)](z)$ preserves the properties of
$S^*_{\Omega}(A,B)$, as well as strong and almost spirallikeness of
type $\beta$ and order $\alpha$ on $B^{n}$. Thus, the mappings in
$S^*_{\Omega}(A,B)$, as well as strong and almost spirallike
mappings, can be constructed through the corresponding functions in
one complex variable. The conclusions follow some special cases and
contain the elementary results. |
Keywords： |
Biholomorphic mappings, Spirallike mappings, Starlike mappings,
Roper-Suffridge operator |
Classification： |
32A30, 30C45 |
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