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

Abstract

This paper addresses coefficient problems for the apple-like convex subclass ${\mathcal{C}}_{\mathcal{A}\mathcal{P}}$, defined by the subordination relation $1+z{f}^{\prime \prime }(z)/f^{\prime }(z)\prec e^z\sqrt{1+z}$. We determine sharp bounds for the initial inverse logarithmic coefficients ${\Gamma }_1$, ${\Gamma }_2$, ${\Gamma }_3$, and the consecutive modulus difference $|{\Gamma }_2|-|{\Gamma }_1|$. 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.