Sharp coefficient Estimates for the class ${\mathcal{S}}_{\mathcal{A}\mathcal{P}}^{\ast }$

We investigate several classic coefficient problems for the Ma–Minda starlike subclass ${\mathcal{S}}_{\mathcal{A}\mathcal{P}}^{\ast }$ defined by the apple-like subordination function ${\psi }_{\mathcal{A}\mathcal{P}}(z)=e^z\sqrt{1+z}$. Sharp bounds are derived for the initial inverse logarithmic coefficients ${\mathrm{\Gamma }}_1$, ${\mathrm{\Gamma }}_2$, ${\mathrm{\Gamma }}_3$, and the successive modulus difference $\mathrm{\mid }{\mathrm{\Gamma }}_2\mathrm{\mid }-\mathrm{\mid }{\mathrm{\Gamma }}_1\mathrm{\mid }$. 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.