Note on the Fekete--Szegö problem for spirallike mappings in Banach spaces

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 \cite{LX} published recently in the journal {\it Results in Mathematics}. We show that on...

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Bibliographic Details
Published in:arXiv.org 2022-01
Main Authors: Elin, Mark, Jacobzon, Fiana
Format: Article
Language:English
Subjects:
Banach spaces
Complex variables
Mathematical analysis
Online Access:Get full text
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Summary: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 \cite{LX} published recently in the journal {\it Results in Mathematics}. We show that one of the theorems in \cite{LX} 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--Szeg\"{o} functional over spirallike mappings in a general Banach space can be deduced from a result in \cite{LX}.
ISSN:2331-8422