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

Abstract

This paper addresses coefficient problems for the apple-like convex subclass $\mathcal{C}_{\mathcal{AP}}$, defined by the subordination relation $1+zf''(z)/f'(z) \prec e^z\sqrt{1+z}$. We determine sharp bounds for the initial inverse logarithmic coefficients $Γ_1$, $Γ_2$, $Γ_3$, and the consecutive modulus difference $|Γ_2|-|Γ_1|$. 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.