Abstract
In this note we present a remark on the paper “On the coefficient inequalities for a class of holomorphic mappings associated with spirallike mappings in several complex variables” by Y. Lai and Q. Xu [10] published recently in the journal Results in Mathematics. We show that one of the theorems in [10] concerning the finite-dimensional space \({{\mathbb {C}}}^n\) is a direct consequence of another one, so it does not need an independent proof. Moreover, we prove that a sharp norm estimate on the Fekete–Szegö functional over spirallike mappings in a general Banach space can be deduced from a result in [10].
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Elin, M., Jacobzon, F. Note on the Fekete–Szegö Problem for Spirallike Mappings in Banach Spaces. Results Math 77, 137 (2022). https://doi.org/10.1007/s00025-022-01672-x
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DOI: https://doi.org/10.1007/s00025-022-01672-x
Keywords
- Fekete–Szegö inequality
- holomorphic mappings
- spirallike mappings of type \(\beta \)
- sharp coefficient bound