Sharp coefficient Estimates for the class $\mathcal{S}_{\mathcal{AP}}^{*}$

Abstract: We investigate several classic coefficient problems for the Ma--Minda starlike subclass $\mathcal{S}{\mathcal{AP}}^{*}$ defined by the apple-like subordination function $ψ{\mathcal{AP}}(z)=e^{z}\sqrt{1+z}$. Sharp bounds are derived for the initial inverse logarithmic coefficients $Γ_1$, $Γ_2$, $Γ_3$, and the successive modulus difference $|Γ_2|-|Γ_1|$. In addition, we evaluate the second-order inverse logarithmic Hankel determinant, the generalized Fekete--Szegö functional over all real parameter domains, and the third-order Hermitian--Toeplitz determinant. The corresponding extremal functions are explicitly determined for each functional.