Coefficient Problems and Sharp Determinant Estimates for the Class $\mathcal{S}^*_{q_1}$

Pradip Das; Nabadwip Sarkar

Coefficient Problems and Sharp Determinant Estimates for the Class $\mathcal{S}^*_{q_1}$

Complex Variables 2026-07-28 v1

Authors: Pradip Das , Nabadwip Sarkar

Abstract

In this paper, we investigate coefficient-related problems for a subclass of normalized analytic functions $\mathcal{S}^*_{q_1}$ , defined by the subordination conditions $\frac{f'(z)}{q_1(z)} \prec 1+\sin z \quad \text{and} \quad q_1(z) \prec e^z,\qquad z\in\mathbb{D}.$ Sharp bounds are obtained for the logarithmic and inverse logarithmic coefficients, as well as for their absolute differences. Moreover, sharp estimates are derived for the second-order Hankel and Hermitian--Toeplitz determinants associated with these coefficients. These results extend and refine several known bounds for related subclasses of analytic functions.

Cite

@article{arxiv.2607.25280,
  title  = {Coefficient Problems and Sharp Determinant Estimates for the Class $\mathcal{S}^*_{q_1}$},
  author = {Pradip Das and Nabadwip Sarkar},
  journal= {arXiv preprint arXiv:2607.25280},
  year   = {2026}
}