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

Sujoy Majumder; Abhijit Banerjee; Goutam Haldar; Shantanu Panja

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arXiv · 2610.16310

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

Sujoy Majumder·Abhijit Banerjee·Goutam Haldar·Shantanu Panja

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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.

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Sujoy Majumder, Abhijit Banerjee, Goutam Haldar, Shantanu Panja. 2026-10-12. 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. https://arxiv.org/abs/2610.16310

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