Directional Coefficient Inequalities for Strongly Starlike Mappings in Complex Banach Spaces

@misc{das2026directional,
  title = {{Directional Coefficient Inequalities for Strongly Starlike Mappings in Complex Banach Spaces}},
  author = {Pradip Das and Nabadwip Sarkar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20849},
  eprint = {2610.20849},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20849},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Directional Coefficient Inequalities for Strongly Starlike Mappings in Complex Banach Spaces
AU  - Pradip Das
AU  - Nabadwip Sarkar
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20849
UR  - https://arxiv.org/abs/2610.20849
AB  - We study a class of strongly starlike mappings of order α on the open unit ball of a complex Banach space under a scalar-profile condition. Using a slice reduction along one-dimensional complex subspaces, we prove a coefficient correspondence theorem identifying the directional coefficients with the Taylor coefficients of an associated one-variable strongly starlike function. We further prove a lifting theorem showing that every one-variable strongly starlike function can be realized by a scalar-profile Banach-space mapping. Consequently, the extremal problems for polynomial directional coefficient functionals coincide exactly with their one-variable counterparts. We apply this correspondence to obtain bounds for |A_2A_3 − A_4|, |A_2A_4 − A_3^2|, and |A_3 − A_2^2|, together with the corresponding estimates for |A_4| and |A_5|. We also establish a parameterized Fekete--Szegő estimate and a sharp bound for the second Hankel determinant of directional logarithmic coefficients.
ER  -