Inverse Logarithmic Coefficients and Associated Sharp Estimates for the Apple-Like Convex Subclass ${\mathcal{C}}_{\mathcal{A}\mathcal{P}}$

This paper addresses coefficient problems for the apple-like convex subclass ${\mathcal{C}}_{\mathcal{A}\mathcal{P}}$, defined by the subordination relation $1+z{f}^{\mathrm{\prime }\mathrm{\prime }}(z)\mathrm{/}{f}^{\mathrm{\prime }}(z)\prec e^z\sqrt{1+z}$. We determine sharp bounds for the initial inverse logarithmic coefficients ${\mathrm{\Gamma }}_1$, ${\mathrm{\Gamma }}_2$, ${\mathrm{\Gamma }}_3$, and the consecutive modulus difference $\mathrm{\mid }{\mathrm{\Gamma }}_2\mathrm{\mid }-\mathrm{\mid }{\mathrm{\Gamma }}_1\mathrm{\mid }$. We also obtain the sharp upper bound for the second-order inverse logarithmic Hankel determinant, characterize the generalized Fekete–Szegő functional for all real parameters, and compute sharp bounds for the third-order Hermitian–Toeplitz determinant. Extremal functions are given for each case.