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

@misc{majumder2026feketeszegö,
  title = {{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}},
  author = {Sujoy Majumder and Abhijit Banerjee and Goutam Haldar and Shantanu Panja},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16310},
  eprint = {2610.16310},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16310},
}

TY  - UNPB
TI  - 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
AU  - Sujoy Majumder
AU  - Abhijit Banerjee
AU  - Goutam Haldar
AU  - Shantanu Panja
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16310
UR  - https://arxiv.org/abs/2610.16310
AB  - 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 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.
ER  -