Abstract:In this paper, we investigate several classical coefficient problems for the geometric subclass $\mathcal{S}_{ex}^{\ast}$ of normalized analytic starlike functions defined by the exponential subordination condition \[ \frac{zf'(z)}{f(z)} \prec e^{\alpha z}, \qquad 0 < \alpha \le 1. \] We determine sharp upper bounds for the initial inverse logarithmic coefficients $\Gamma_1$, $\Gamma_2$, and $\Gamma_3$, and establish sharp upper and lower bounds for the consecutive difference $|\Gamma_2| - |\Gamma_1|$. Furthermore, we derive sharp estimates for the second-order inverse logarithmic Hankel determinant $H_{2,1}(F_{f^{-1}}/2)$ and obtain sharp upper and lower bounds for the third-order Hermitian--Toeplitz determinant $T_{3,1}(f)$. Finally, we provide a complete solution to the extremal problem for the generalized Fekete--Szegő functional \[ |a_3 - \lambda a_2^2| - \mu |a_2|. \] In each problem considered, the obtained estimates are shown to be sharp, and the corresponding extremal functions are explicitly characterized.
From: Pradip Das Mr. [view email]
[v1]
Mon, 8 Jun 2026 21:24:41 UTC (21 KB)
[v2]
Mon, 22 Jun 2026 06:23:35 UTC (1 KB) (withdrawn)
[v3]
Wed, 24 Jun 2026 22:34:12 UTC (23 KB)
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