Abstract
Let X be a complex Banach space with norm ‖ · ‖, B be the unit ball in X, Dn be the unit polydisc in ℂn. In this paper, we introduce a class of holomorphic mappings \( \mathcal{M}_g \) on B or Dn. Let f(x) be a normalized locally biholomorphic mapping on B such that (Df(x))−1f(x) ∈ \( \mathcal{M}_g \) and f(x) − x has a zero of order k + 1 at x = 0. We obtain coefficient estimates for f(x). These results unify and generalize many known results.
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