The Fekete-Szegö problem for starlike mappings of order $α$ and quasi-convex mappings of type $B$ in the unit balls of complex Banach spaces
Year: 2026
Type: preprint
Abstract: We establish sharp estimates for the generalized Zalcman functional corresponding to the index $n=2$ for normalized starlike mappings of order $α$ and normalized quasi-convex mappings of type $B$ in the unit ball of a complex Banach space and on the unit polydisk in $\mathbb{C}^n$. We also derive sharp Fekete-Szegö inequalities for normalized starlike mappings of order $α$ and normalized quasi-convex mappings of type $B$ in the unit ball of a complex Banach space. Our results extend classical coefficient estimates to higher-dimensional holomorphic mappings and provide a partial confirmation of the generalized Zalcman conjecture in higher dimensions.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221799237