Estimates for a Parameterized Hankel Functional of Starlike Mappings of Order α and Quasi-Convex Mappings of Type B in Complex Banach Spaces

@misc{majumder2026estimates,
  title = {{Estimates for a Parameterized Hankel Functional of Starlike Mappings of Order $α$ and Quasi-Convex Mappings of Type $B$ in Complex Banach Spaces}},
  author = {Sujoy Majumder and Abhijit Banerjee and Shantanu Panja and Debabrata Pramanik},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33031},
  eprint = {2610.33031},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33031},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Estimates for a Parameterized Hankel Functional of Starlike Mappings of Order α and Quasi-Convex Mappings of Type B in Complex Banach Spaces
AU  - Sujoy Majumder
AU  - Abhijit Banerjee
AU  - Shantanu Panja
AU  - Debabrata Pramanik
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.33031
UR  - https://arxiv.org/abs/2610.33031
AB  - In this paper, we introduce and investigate a parameterized Hankel-type functional H_2,2^μ(f)=μa_2a_4−a_3^2, μ∈[0,1], which reduces to the classical second-order Hankel determinant H_2,2(f) when μ=1. We obtain estimates for H_2,2^μ(f) over the class of starlike mappings of order α on the unit ball of a complex Banach space and on the unit polydisk 𝕌^n in ℂ^n. We also establish estimates for H_2,2^μ(f) over the class of quasi-convex mappings of type B on the unit ball of a complex Banach space and on the unit polydisk 𝕌^n. For μ=1, our results recover the corresponding estimates for the classical Hankel determinant and extend the known one-dimensional results of Cho et al. \cite{Cho-2018} and Thomas et al. \cite{Thomas-Tuneski} to higher-dimensional settings.
ER  -