The Estimates of All Homogeneous Expansions for a Subclass of ε Quasi-convex Mappings in Several Complex Variables

Abstract

The authors obtain the estimates of all homogeneous expansions for a subclass of ε 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 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 / ε quasi-convex mapping / ε starlike mapping / Starlike mapping / Quasi-convex mapping / Quasi-convex mappings of type $\mathbb{A}$

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