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| The Estimates of All Homogeneous Expansions for a Subclass of ε Quasi-convex Mappings in Several Complex Variables |
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Citation： |
Xiaosong LIU,Taishun LIU.The Estimates of All Homogeneous Expansions for a Subclass of ε Quasi-convex Mappings in Several Complex Variables[J].Chinese Annals of Mathematics B,2018,39(4):621~632 |
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Net amount： 789 |
Authors： |
Xiaosong LIU; Taishun LIU |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (No.11471111) and the Guangdong Provincial
Natural Science Foundation of China (No.2014A030307016). |
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| Abstract： |
The authors obtain the estimates of all homogeneous expansions for a
subclass of $\varepsilon$ quasi-convex mappings on the unit ball in
complex Banach spaces. Moreover, the estimates of all homogeneous
expansions for the above generalized mappings on the unit polydisk
in $\mathbb{C}^n$ are also obtained. Especially, the above estimates
are only sharp for a subclass of starlike mappings, quasi-convex
mappings and quasi-convex mappings of type $\mathbb{A}$. The results
are the generalization of many known results. |
Keywords： |
Homogeneous expansion, $varepsilon$ quasi-convex mapping,$varepsilon$ starlike mapping, Starlike mapping, Quasi-convexmapping, Quasi-convex mappings of type $mathbb{A}$ |
Classification： |
32A30, 32H02 |
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