Abstract
A refining estimation of homogeneous expansion for f is discussed, where f belongs to a subclass of all normalized biholomorphic mappings defined on the unit polydisk in C n or the unit ball in complex Banach spaces, and x =0 is a zero of order k +1 of f ( x )- x . Moreover, an estimation of homogeneous expansion for subordinate mappings defined on the unit ball in complex Banach spaces is also given.
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